Optical system

ABSTRACT

Optical systems including a partial reflector, a reflective polarizer, and a quarter wave retarder disposed between the partial reflector and the reflective polarizer are described. The reflective polarizer is curved about two orthogonal axes and has at least one location having a radial distance r 1  from an optical axis passing through an apex of the reflective polarizer and a displacement s 1  from a plane perpendicular to the optical axis at an apex of the reflective polarizer, where s 1 /r 1  is at least 0.1. The optical system is adapted to provide an adjustable dioptric correction.

BACKGROUND

Display systems may include a beam splitter, a quarter wave retarder anda reflective polarizer.

U.S. Pat. No. 7,242,525 (Dike) describes an optical system that projectsa real image into space and includes one or more features located alongthe optical path that enhance the viewability of the real image. Theoptical system includes a converging element for converging a portion ofsource light so as to form the real image.

U.S. Pat. No. 6,271,969 (Mertz) describes an optical collimatingassembly for imaging light from a display. The optical assembly includesfirst and second linear polarization filters having polarizationdirections that are orthogonal to one another. A folded imaging assemblythat includes a first beam splitter, a first ¼ wave plate, and a secondbeam splitter is located between the polarization filters.

U.S. Pat. No. 8,780,039 (Gay et al.) describes an optical system forvarying the shape of a surface in which an image displayed by thedisplay device is perceived. The optical system comprises first andsecond spaced-apart partial reflectors, at least one of which isswitchable between a first non-flat shape and a second different shape,which may be flat or non-flat. The reflectors, together withpolarization optics, provide a light path such that light from thedisplay is at least partially transmitted by the first reflector,partially reflected by the second reflector, partially reflected by thefirst reflector and partially transmitted by the second reflector.

Reflective polarizers may be multilayer optical films. U.S. Pat. No.6,916,440 (Jackson et al.) describes a process for stretching multilayeroptical films in a uniaxial fashion. U.S. Pat. No. 6,788,463 (Merrill etal.) describes post-formed multilayer optical films.

SUMMARY

In some aspects of the present description, an optical system includingan image surface, a stop surface, a first optical stack disposed betweenthe image surface and the stop surface, and a second optical stackdisposed between the first optical stack and the stop surface isprovided. The first optical stack is convex toward the image surfacealong orthogonal first and second axes, and includes a first opticallens and a partial reflector having an average optical reflectance of atleast 30% in a desired plurality of wavelengths. The second opticalstack is convex toward the image surface along the first and secondaxes, and includes a second optical lens, a multilayer reflectivepolarizer substantially transmitting light having a first polarizationstate and substantially reflecting light having an orthogonal secondpolarization state, and a first quarter wave retarder disposed betweenthe reflective polarizer and the first optical stack.

In some aspects of the present description, an optical system includingan image surface, a stop surface, a first optical stack disposed betweenthe image surface and the stop surface, and a second optical stackdisposed between the first optical stack and the stop surface isprovided. The first optical stack includes a first optical lens, and apartial reflector having an average optical reflectance of at least 30%in a desired plurality of wavelengths. The second optical stack includesa second optical lens, a multilayer reflective polarizer including atleast one layer substantially optically biaxial at at least one firstlocation on the at least one layer away from an optical axis of thesecond optical stack and substantially optically uniaxial at at leastone second location away from the optical axis, and a first quarter waveretarder disposed between the reflective polarizer and the first opticalstack. Substantially any chief light ray that passes through the imagesurface and the stop surface is incident on each of the first opticalstack and the second optical stack with an angle of incidence less thanabout 30 degrees.

In some aspects of the present description, an optical system includingan image source emitting an undistorted image, an exit pupil, a partialreflector and a reflective polarizer is provided. The partial reflectorhas a first shape convex toward the image source along orthogonal firstand second axes and has an average optical reflectance of at least 30%in a pre-determined plurality of wavelengths. The reflective polarizerhas a different second shape convex toward the image source along thefirst and second axes, such that a distortion of the emitted undistortedimage transmitted by the exit pupil is less than about 10%.

In some aspects of the present description, an optical system includingan image source, an exit pupil, a first optical stack disposed betweenthe image source and the exit pupil, and a second optical stack disposedbetween the first optical stack and the exit pupil is provided. Thefirst optical stack includes a first optical lens, and a partialreflector having an average optical reflectance of at least 30% in adesired plurality of wavelengths. The second optical stack includes asecond optical lens, a multilayer reflective polarizer, and a firstquarter wave retarder disposed between the reflective polarizer and thefirst optical stack. Substantially any chief light ray having at leastfirst and second wavelengths at least 150 nm apart in the desiredplurality of wavelengths and emitted by the image source and transmittedby the exit pupil has a color separation distance at the exit pupil ofless than 1.5 percent of a field of view at the exit pupil.

In some aspects of the present description, an optical system includingan image source, an exit pupil, a first optical stack disposed betweenthe image source and the exit pupil, and a second optical stack disposedbetween the first optical stack and the exit pupil is provided. Thefirst optical stack includes a first optical lens, and a partialreflector having an average optical reflectance of at least 30% in adesired plurality of wavelengths. The second optical stack includes asecond optical lens, a multilayer reflective polarizer, and a firstquarter wave retarder disposed between the reflective polarizer and thefirst optical stack. Substantially any chief light ray having at leastfirst and second wavelengths at least 150 nm apart in the desiredplurality of wavelengths and emitted by the image source and transmittedby the exit pupil has a color separation distance at the exit pupil ofless than 20 arc minutes.

In some aspects of the present description, an optical system includingan image surface having a maximum lateral dimension A, a stop surfacehaving a maximum lateral dimension B, and an integral optical stackdisposed between the image surface and the stop surface is provided. A/Bis at least 3. The integral optical stack includes a first optical lens,a partial reflector having an average optical reflectance of at least30% in a pre-determined plurality of wavelengths, a multilayerreflective polarizer substantially transmitting light having a firstpolarization state and substantially reflecting light having anorthogonal second polarization state, and a first quarter wave retarderat at least one wavelength in the pre-determined plurality ofwavelengths. At least one chief light ray transmitted through the stopsurface and the image surface passes through the stop surface at anincident angle of at least 40 degrees. An integral optical stack may bedescribed as an optical stack with the various components and layers inthe optical stack formed together or adhered together, for example.

In some aspects of the present description, an optical system includingan image surface, a substantially planar stop surface, and, disposedbetween the image surface and the stop surface, first, second and thirdoptical lenses, a partial reflector having an average opticalreflectance of at least 30% in a pre-determined plurality ofwavelengths, a multilayer reflective polarizer substantiallytransmitting light having a first polarization state and substantiallyreflecting light having an orthogonal second polarization state, and afirst quarter wave retarder at at least one wavelength in thepre-determined plurality of wavelengths is provided. The optical systemincludes a plurality of major surfaces disposed between the imagesurface and the stop surface, each major surface convex toward the imagesurface along orthogonal first and second axes, and at least sixdifferent major surfaces have six different convexities.

In some aspects of the present description, a thermoformed multilayerreflective polarizer substantially rotationally symmetric about anoptical axis passing thorough an apex of the thermoformed multilayerreflective polarizer and convex along orthogonal first and second axesorthogonal to the optical axis is provided. The thermoformed multilayerreflective polarizer has at least one inner layer substantiallyoptically uniaxial at at least one first location away from the apex,and at least one first location on the reflective polarizer having aradial distance, r1, from the optical axis and a displacement, s1, froma plane perpendicular to the optical axis at the apex, where s1/r1 is atleast 0.2.

In some aspects of the present description, a thermoformed multilayerreflective polarizer substantially rotationally symmetric about anoptical axis passing thorough an apex of the thermoformed multilayerreflective polarizer and convex along orthogonal first and second axesorthogonal to the optical axis is provided. The thermoformed multilayerreflective polarizer has at least one first location on the reflectivepolarizer having a radial distance, r1, from the optical axis and adisplacement, s1, from a plane perpendicular to the optical axis at theapex, where s1/r1 is at least 0.2. For an area of the reflectivepolarizer defined by s1 and r1, a maximum variation of a transmissionaxis of the reflective polarizer is less than about 2 degrees.

In some aspects of the present description, a method of making anoptical stack is provided. The method includes the steps of providing athermoform tool centered on a tool axis and having an external surfacerotationally asymmetric about the tool axis; heating an optical filmresulting in a softened optical film; conforming the softened opticalfilm to the external surface while stretching the softened film along atleast orthogonal first and second directions away from the tool axisresulting in a conformed optical film rotationally asymmetric about anoptical axis of the conformed film, where the optical axis coincidentwith the tool axis; cooling the conformed optical film resulting in asymmetric optical film rotationally symmetric about the optical axis;and molding an optical lens on the symmetric optical film resulting inthe optical stack.

In some aspects of the present description, a method of making a desiredoptical film having a desired shape is provided. The method includes thesteps of providing a thermoform tool having an external surface having afirst shape different than the desired shape; heating an optical filmresulting in a softened optical film; conforming the softened opticalfilm to the external surface having the first shape while stretching thesoftened film along at least orthogonal first and second directionsresulting in a conformed optical film having the first shape; andcooling the conformed optical film resulting in the desired optical filmhaving the desired shape.

In some aspects of the present description, an optical system includingan image surface, a stop surface, a first optical stack disposed betweenthe image surface and the stop surface, and a second optical stackdisposed between the first optical stack and the exit pupil is provided.The first optical stack includes a first optical lens, and a partialreflector having an average optical reflectance of at least 30% in adesired plurality of wavelengths. The second optical stack includes asecond optical lens, a thermoformed multilayer reflective polarizerrotationally symmetric about an optical axis of the second optical stackand convex toward the image source along orthogonal first and secondaxes orthogonal to the optical axis, and a first quarter wave retarderdisposed between the reflective polarizer and the first optical stack.The thermoformed multilayer reflective polarizer has at least one firstlocation having a radial distance, r1, from an optical axis passingthrough an apex of the thermoformed multilayer reflective polarizer, anda displacement, s1, from a plane perpendicular to the optical axis atthe apex, where s1/r1 is at least 0.1.

In some aspects of the present description, an optical stack isprovided. The optical stack includes a first lens, a second lensadjacent the first lens, a quarter wave retarder disposed between thefirst and second lenses, a reflective polarizer disposed on the secondlens opposite the first lens, and a partial reflector disposed on thefirst lens opposite the second lens. The reflective polarizer is curvedabout two orthogonal axes, and the optical stack is an integral opticalstack.

In some aspects of the present description, an optical system includinga partial reflector, a multilayer reflective polarizer, and a firstquarter wave retarder disposed between the partial reflector and themultilayer reflective polarizer is provided. The partial reflector hasan average optical reflectance of at least 30% in a desired plurality ofwavelengths. The multilayer reflective polarizer substantially transmitslight having a first polarization state and substantially reflects lighthaving an orthogonal second polarization state. The multilayerreflective polarizer is convex along orthogonal first and second axes,and has at least one first location on the multilayer reflectivepolarizer having a radial distance r1 from an optical axis of themultilayer reflective polarizer and a displacement s1 from a planeperpendicular to the optical axis at an apex of the multilayerreflective polarizer, where s1/r1 is at least 0.1. The multilayerreflective polarizer comprises at least one layer substantiallyoptically biaxial at at least one first location on the at least onelayer away from the optical axis and substantially optically uniaxial atat least one second location away from the optical axis.

In some aspects of the present description, an optical system includinga first optical stack, a second optical stack disposed adjacent to thefirst optical stack and convex along orthogonal first and second axes,and a first quarter wave retarder disposed between the second opticalstack and the first optical stack is provided. The first optical stackincludes a first optical lens and a partial reflector having an averageoptical reflectance of at least 30% in a desired plurality ofwavelengths. The second optical stack includes a second optical lens,and a multilayer reflective polarizer substantially transmitting lighthaving a first polarization state and substantially reflecting lighthaving an orthogonal second polarization state. The reflective polarizerincludes at least one first location on the multilayer reflectivepolarizer having a radial distance r1 from an optical axis of the secondoptical stack and a displacement s1 from a plane perpendicular to theoptical axis at an apex of the multilayer reflective polarizer, wheres1/r1 is at least 0.1. The multilayer reflective polarizer includes atleast one layer substantially optically biaxial at at least one firstlocation on the at least one layer away from the optical axis andsubstantially optically uniaxial at at least one second location awayfrom the optical axis.

In some aspects of the present description, an optical system includinga first optical stack, a second optical stack disposed adjacent to thefirst optical stack and convex along orthogonal first and second axes,and a first quarter wave retarder disposed between the second opticalstack and the first optical stack is provided. The first optical stackincludes a first optical lens and a partial reflector having an averageoptical reflectance of at least 30% in a desired plurality ofwavelengths. The second optical stack includes a second optical lens, areflective polarizer substantially transmitting light having a firstpolarization state and substantially reflecting light having anorthogonal second polarization state. The reflective polarizer has atleast one first location on the multilayer reflective polarizer having aradial distance r1 from an optical axis of the second optical stack anda displacement s1 from a plane perpendicular to the optical axis at anapex of the reflective polarizer, where s1/r1 is at least 0.1. Theoptical system has a contrast ratio of at least 50 over a field of viewof the optical system.

In some aspects of the present description, an optical system includinga first optical stack, a second optical stack disposed adjacent to thefirst optical stack and convex along orthogonal first and second axes,and a first quarter wave retarder disposed between the second opticalstack and the first optical stack is provided. The first optical stackincludes a first optical lens and a partial reflector having an averageoptical reflectance of at least 30% in a desired plurality ofwavelengths. The second optical stack includes a second optical lens anda reflective polarizer substantially transmitting light having a firstpolarization state and substantially reflecting light having anorthogonal second polarization state. At least one first location on thereflective polarizer has a radial distance r1 from an optical axis ofthe second optical stack and a displacement s1 from a planeperpendicular to the optical axis at an apex of the reflectivepolarizer, where s1/r1 is at least 0.1. The optical system is adapted toprovide an adjustable dioptric correction.

In some aspects of the present description, a head-mounted displayincluding first and second optical systems is provided. The firstoptical system includes a first image surface, a first exit pupil, afirst reflective polarizer disposed between the first exit pupil and thefirst image surface, and a first quarter wave retarder disposed betweenthe first reflective polarizer and the first partial reflector. Thefirst reflective polarizer is convex about two orthogonal axes. Thefirst partial reflector is disposed between the first reflectivepolarizer and the first image surface, and the first partial reflectorhas an average optical reflectance of at least 30% in a pre-determinedplurality of wavelengths. The second optical system includes a secondimage surface, a second exit pupil, a second reflective polarizerdisposed between the second exit pupil and the second image surface, asecond partial reflector disposed between the second reflectivepolarizer and the second image surface, and a second quarter waveretarder disposed between the second reflective polarizer and the secondpartial reflector. The second reflective polarizer is convex about twoorthogonal axes. The second partial reflector has an average opticalreflectance of at least 30% in the pre-determined plurality ofwavelengths.

In some aspects of the present description, a camera including anaperture and an image recording device is provided. The camera includesa reflective polarizer disposed between the aperture and the imagerecording device. The reflective polarizer is curved about twoorthogonal axes. A partial reflector having a having an average opticalreflectance of at least 30% in a pre-determined plurality of wavelengthsis disposed between the reflective polarizer and the image recordingdevice. A quarter wave retarder disposed between the reflectivepolarizer and the partial reflector.

In some aspects of the present description, a beam expander is provided.The beam expander includes a partial reflector having a having anaverage optical reflectance of at least 30% in a pre-determinedplurality of wavelengths, a reflective polarizer disposed adjacent toand spaced apart from the partial reflector, and a quarter wave retarderdisposed between the reflective polarizer and the partial reflector. Thereflective polarizer curved about two orthogonal axes.

In some aspects of the present description, a projection systemincluding a light source, an image forming device disposed to receivelight from the light source and emit a converging patterned light, and abeam expander is provided. The beam expander includes a partialreflector having a having an average optical reflectance of at least 30%in a pre-determined plurality of wavelengths, a reflective polarizerdisposed adjacent to and spaced apart from the partial reflector, and aquarter wave retarder disposed between the reflective polarizer and thepartial reflector. The reflective polarizer curved about two orthogonalaxes. The beam expander is disposed such that the converging patternedlight from the image forming device is incident on the partial reflectorand the beam expander transmits a diverging patterned light.

In some aspects of the present description an illuminator including abeam expander, a polarizing beam splitter, a light source and areflective component is provided. The beam expander includes areflective polarizer curved about two orthogonal directions.

The polarizing beam splitter includes a first prism having an inputface, an output face and a first hypotenuse; a second prism having afirst face and a second hypotenuse with the second hypotenuse disposedadjacent the first hypotenuse; and a second reflective polarizerdisposed between the first hypotenuse and the second hypotenuse. Thelight source is disposed adjacent the input face and defines an inputactive area on the input face. The reflective component is disposedadjacent the first face for receiving light emitted from the lightsource and emitting a converging light. The reflective component has alargest active area which defines an output active area on the outputface. The beam expander is disposed to receive the converging light andtransmit a diverging light. One or both of the input active area and theoutput active area are less than about half the largest active area ofthe reflective component.

In some aspects of the present description, a magnifying deviceincluding an optical system is provided. The optical system includes anexit pupil, a reflective polarizer proximate the exit pupil and curvedabout two orthogonal axes, a partial reflector disposed adjacent thereflective polarizer opposite the exit pupil and spaced apart from thereflective polarizer. The partial reflector has a having an averageoptical reflectance of at least 30% in a pre-determined plurality ofwavelengths. A quarter wave retarder is disposed between the reflectivepolarizer and the partial reflector.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1-2 are schematic cross-sectional views of optical systems;

FIGS. 3A-4C are cross-sectional views of portions of optical stacks;

FIGS. 5-9 are schematic cross-sectional views of optical systems;

FIG. 10 is a cross-sectional view of a reflective polarizer;

FIG. 11 is a front view of a reflective polarizer;

FIG. 12 is a cross-sectional view of a reflective polarizer;

FIG. 13A is a front view of a reflective polarizer;

FIG. 13B is a cross-sectional view of the reflective polarizer of FIG.13A;

FIG. 14 is a plot of contrast ratio of an optical system versus apolarization accuracy of the optical system;

FIG. 15 is a schematic flow chart illustrating a method of making adesired optical film having a desired shape;

FIG. 16 is a schematic cross-sectional view of a thermoform tool;

FIG. 17 is a schematic top view of a head-mounted display;

FIGS. 18-23 are cross-sectional views of optical systems;

FIGS. 24A-24C are schematic top views of devices including one or moreoptical systems;

FIG. 25 is a schematic side view of a device including an illuminatorand a beam expander;

FIG. 26 is a schematic cross-sectional view of an optical stack;

FIG. 27A is a side view of an optical system of a head-mounted display;

FIGS. 27B-27C are top views of the optical system of FIG. 27A; and

FIGS. 28A-28B are cross-sectional views of a toric lens in differentplanes.

DETAILED DESCRIPTION

In the following description, reference is made to the accompanyingdrawings that forms a part hereof and in which various embodiments areshown by way of illustration. The drawings are not necessarily to scale.It is to be understood that other embodiments are contemplated and maybe made without departing from the scope or spirit of the presentdisclosure. The following detailed description, therefore, is not to betaken in a limiting sense.

According to the present description, it has been found that opticalsystems including a reflective polarizer that is convex about twoorthogonal axes and disposed between a stop surface (e.g., an exit pupilor an entrance pupil) and an image surface (e.g., a surface of a displaypanel or a surface of an image recorder) can provide a system having ahigh field of view, a high contrast, a low chromatic aberration, a lowdistortion, and/or a high efficiency in a compact configuration that isuseful in various devices including head-mounted displays, such asvirtual reality displays, and cameras, such as cameras included in acell phone, for example.

The optical system may include a partial reflector disposed between thereflective polarizer and the image surface and may include at least onequarter wave retarder. For example, a first quarter wave retarder may bedisposed between the reflective polarizer and the partial reflector andin some cases a second quarter wave retarder may be disposed between thepartial reflector and the image surface. The optical systems may beadapted to utilize wavelengths in a desired or pre-determined pluralityof wavelengths and the partial reflector may have an average opticalreflectance of at least 30% in the desired or pre-determined pluralityof wavelengths and may have an average optical transmittance of at least30% in the desired or pre-determined plurality of wavelengths. Thequarter wave retarder(s) may be quarter wave retarder(s) at at least onewavelength in the desired or pre-determined plurality of wavelengths. Insome embodiments, the desired or pre-determined plurality of wavelengthsmay be a single continuous range of wavelengths (e.g., a visible rangeof 400 nm to 700 nm) or it may be a plurality of continuous ranges ofwavelengths. The partial reflector may be a notch reflector and thedesired or pre-determined plurality of wavelengths may include one ormore wavelength ranges at least some of which having a full width athalf maximum reflection band of no more than 100 nm or no more than 50nm. The reflective polarizer may be a notch reflective polarizer and mayhave reflection bands that match or substantially match reflection thebands of the partial reflector. In some cases, the optical system may beadapted for use with one or more lasers and the plurality of desired orpredetermined wavelengths may include narrow band(s) (e.g., 10 nm inwidth) about the laser(s) wavelength(s).

The reflective polarizer, the partial reflector and/or the quarter waveretarder(s) may also be curved about two orthogonal axes. In someembodiments, each of the reflective polarizer, the first quarter waveretarder and partial reflector are curved about two orthogonal axes, andin some embodiments, each of these layers or components are convextoward the image surface. In some embodiments, a plurality of surfacesare provided between the stop surface and the image surface, and each ofthe reflective polarizer, the first quarter wave retarder and partialreflector are disposed on one of the surfaces. These layers orcomponents may be each disposed on different surfaces, or two or more ofthe layers components may be disposed on a single surface. In someembodiments, one, two, three, or more lenses are disposed between thestop surface and the image surface and the plurality of surfaces mayinclude the major surfaces of the one or more lenses. One or more of thelenses may be positioned between the reflective polarizer and thepartial reflector, one or more of the lenses may be positioned betweenthe stop surface and reflective polarizer, and one or more of the lensesmay be position between the partial reflector and the image surface.

The reflective polarizer may be a thermoformed reflective polarizer andmay be a thermoformed polymeric multilayer optical film reflectivepolarizer or may be a thermoformed wire grid polarizer, for example.Thermoforming refers to a forming process carried out above ambienttemperature. Conventional display designs incorporating a reflectivepolarizer either use a flat reflective polarizer or use a reflectivepolarizer disposed in a cylindrically curved shape which is curved abouta single axis. Curving a reflective polarizer into a cylindrical shapedoes not stretch the reflective polarizer and so does not substantiallyalter its performance as a reflective polarizer. The reflectivepolarizers of the present description may be curved about two orthogonalaxes and may be stretched as a result of forming the reflectivepolarizer into the curved shape. According to the present description,it has been found that such compound curved reflective polarizers can beused in optical systems for display and camera applications, forexample, while contributing to various improved optical properties(e.g., reduced color separation, reduced distortion, improved field ofview, improved contrast ratio, etc.) even though the reflectivepolarizer is stretched into the compound curved shape. As discussedfurther elsewhere herein, it has been found that convex reflectivepolarizers made by thermoforming polymeric multilayer optical film thatwas uniaxially oriented prior to thermoforming are particularlyadvantageous when used in the optical systems of the presentdescription. In some embodiments, the uniaxially oriented multilayerreflective polarizers is APF (Advanced Polarizing Film, available from3M Company, St. Paul, Minn.). In some embodiments, optical systemsinclude a thermoformed APF and any or substantially any chief ray in theoptical system that is incident on the thermoformed APF has a low angleof incidence (e.g., less than about 30 degrees, less than about 25degrees, or less than about 20 degrees). FIG. 1 is a schematiccross-sectional view of optical system 100 including image surface 130,stop surface 135, a first optical stack 110 disposed between the imagesurface 130 and the stop surface 135, a second optical stack 120 isdisposed between the first optical stack 110 and the stop surface 135.Each of the first and second optical stacks 110 and 120 are convextoward the image surface 130 along orthogonal first and second axes. Anx-y-z coordinate system is provided in FIG. 1. The orthogonal first andsecond axes may be the x- and y-axes, respectively. The image surface130 has a maximum lateral dimension of A and the stop surface 135 has amaximum lateral dimension of B. The maximum lateral dimension may be adiameter for circular image or stop surfaces or may be a diagonaldistance for rectangular image or stop surfaces. In some embodiments,A/B may be at least 2, at least 3, at least 4, or at least 5. The imagesurface 130 and/or the stop surface 135 may be substantially planar ormay be curved.

The first optical stack 110 includes a first optical lens 112 havingopposing first and second major surfaces 114 and 116 respectively. Thefirst and/or second major surfaces 114 and 116 may have one or morelayers or coatings disposed thereon. The first optical stack 110 alsoincludes a partial reflector disposed on one of the first or secondmajor surfaces 114 and 116, as described further elsewhere herein (see,e.g., FIG. 2 and FIGS. 3A-3C). Any of the partial reflectors included inthe optical systems of the present description may have an averageoptical reflectance of at least 30% in a desired or pre-determinedplurality of wavelengths. The desired or pre-determined plurality ofwavelengths may be a visible wavelength range (e.g., 400 nm to 700 nm),an infrared wavelength range, an ultraviolet wavelength range, or somecombination of visible, infrared and ultraviolet wavelengths. In someembodiments, the desired or pre-determined plurality of wavelengths maybe a narrow wavelength range or a plurality of narrow wavelength rangesand the partial reflector may be a notch reflector having at least onereflection band with a full-width at half maximum of no more than 100 nmor no more than 50 nm. The average optical reflectance can be determinedby averaging the reflectance over the desired or pre-determinedplurality of wavelengths. Similarly, an average optical transmittancecan be determined by averaging the transmittance over the desired orpre-determined plurality of wavelengths. In some embodiments, thepartial reflector has an average optical reflectance and an averageoptical transmittance in the desired or pre-determined plurality ofwavelengths that are each in a range of 30% to 70%, or each in a rangeof 40% to 60%. The partial reflector may be a half mirror, for example.Any suitable partial reflector may be used. For example, the partialreflectors may be constructed by coating a thin layer of a metal (e.g.,silver or aluminum) on a transparent substrate. The partial reflectormay also be formed by depositing thin-film dielectric coatings onto asurface of a lens, or by depositing a combination of metallic anddielectric coatings on the surface of the lens, for example. In someembodiments, the partial reflector may be a second reflective polarizerwhich may be a multilayer polymeric reflective polarizer (e.g., APF orDBEF) or may be a wire grid polarizer.

The second optical stack includes a second optical lens 122 having firstand second major surfaces 124 and 126. The first and/or second majorsurfaces 124 and 126 may have one or more layers or coatings disposedthereon. As described further elsewhere herein (see, e.g., FIG. 2 andFIGS. 4A-4C), the second optical stack 120 may include a reflectivepolarizer and a first quarter wave retarder that are either disposed oneach other (e.g., a quarter wave retarder film (e.g., an orientedpolymer film) laminated to a reflective polarizer film or a quarter waveretarder coating (e.g., a liquid crystal polymer coating on a reflectivepolarizer film) and on one of the first and second major surfaces 124and 126, or the reflective polarizer is disposed on first major surface124 and the first quarter wave retarder is disposed on second majorsurface 126. The first quarter wave retarder may be a film molded withsecond optical lens 122 or may be a coating applied to second majorsurface 126 after the second optical lens 122 has been formed, forexample. Suitable coatings for forming a quarter wave retarder includethe linear photopolymerizable polymer (LPP) materials and the liquidcrystal polymer (LCP) materials described in US Pat. App. Pub. Nos. US2002/0180916 (Schadt et al.), US 2003/028048 (Cherkaoui et al.) and US2005/0072959 (Moia et al.). Suitable LPP materials include ROP-131 EXP306 LPP and suitable LCP materials include ROF-5185 EXP 410 LCP, bothavailable from Rolic Technologies, Allschwil, Switzerland. The quarterwave retarder may be quarter wave at at least one wavelength in thedesired or predetermined plurality of wavelengths.

In some embodiments, the second optical stack 120 includes a reflectivepolarizer on one of the first and second major surfaces 124 and 126. Theoptical system 100 includes a first quarter wave retarder disposedbetween the first and second lenses 112 and 122. The first quarter waveretarder may be disposed on the second surface 126 of the second opticalstack 122 (in which case, it may be considered to be part of secondoptical stack 120 or it may be considered to be disposed between thefirst and second optical stacks 110 and 120), or may be included as aseparate component with spacings between the first and second opticalstacks 110 and 120, or may be disposed on first surface 114 of the firstoptical stack 110 (in which case, it may be considered to be part offirst optical stack 110 or it may be considered to be disposed betweenthe first and second optical stacks 110 and 120).

The multilayer reflective polarizer substantially transmits light havinga first polarization state and substantially reflects light having anorthogonal second polarization state. The first and second polarizationstates may be linear polarization states. The first quarter waveretarder is disposed between the reflective polarizer and the firstoptical stack 110.

The optical stacks of the present description can be made bythermoforming any films included in the optical stack and then injectionmolding a lens onto the films using a film insert molding process, forexample. As described further elsewhere herein, the reflective polarizerfilm may have anisotropic mechanical properties which may make the filmrotationally asymmetric after cooling if it is thermoformed on arotationally symmetric mold. It may be difficult to injection mold arotationally asymmetric film onto a rotationally symmetric lens withoutcausing wrinkling or other defects in the film. It has been found thatusing a rotationally asymmetric thermoform mold can result in arotationally symmetric film after cooling if the film has anisotropicmechanical properties. A rotationally symmetric lens can be insertmolded onto the resulting rotationally symmetric film without wrinklingor otherwise damaging the thermoformed film.

Image surface 130 may be any surface where an image is formed. In someembodiments, an image source comprises the image surface 130 and thestop surface 135 is an exit pupil. For example, image surface 130 may bean output surface of an image forming device such as a display panel.Stop surface 135 may be an exit pupil of optical system 100 and may beadapted to overlap an entrance pupil of a second optical system, whichmay be a viewer's eye or a camera, for example. The entrance pupil ofthe second optical system may be an entrance pupil of a viewer's eye,for example. The image source may emit polarized or unpolarized light.In some embodiments, image surface 130 is an aperture adapted to receivelight reflected from objects external to optical system 100.

The optical system 100 may include one or more additional retarders. Forexample, a second quarter wave retarder may be included in first opticalstack 110 and may be disposed on one of the first and second majorsurfaces 114 and 116 or may be disposed on the partial reflector. It maybe desirable to include the second quarter wave retarder, for example,when the image surface 130 is a surface of a display panel producingpolarized light. The display panel may emit linearly, circularly orelliptically polarized light. For example, the display panel may be aliquid crystal display (LCD) panel or a Liquid Crystal on Silicon (LCoS)display panel and may emit linearly polarized light. In someembodiments, a second quarter wave retarder is disposed between thepartial reflector and the image surface, and in some embodiments alinear polarizer (e.g., a linear absorbing polarizer or a secondreflective polarizer) is disposed between the second quarter waveretarder and the image surface 130. In some embodiments, the displaypanel is substantially flat. In other embodiments a curved display panelis used. For example, a curved OLED (organic light emitting diode)display may be used. In some embodiments, a transparent orsemi-transparent display (e.g., transparent OLED, LCD, orelectrophoretic displays) may be used. In some embodiments, an imagesource comprises the image surface where the image source may include adisplay panel and may optionally include a shutter. In some embodiments,a shutter (e.g., a liquid crystal shutter or a PDLC (polymer dispersedliquid crystal) shutter, or a photochromic shutter, or a physicallyremovable shield that can function as a shutter) may be used with atransparent or semi-transparent display panel to selectively allow ordisallow ambient light to pass through the transparent orsemi-transparent display panel. A semi-transparent display panel mayhave a transmission in at least one state of the display panel of atleast 25 percent, or at least 50 percent for at least one visiblewavelength. In some embodiments, the image source may comprise aflorescent material that can be irradiated with non-visible light toproduce visible images.

In some embodiments, an image recorder comprises the image surface 130and the stop surface 135 is an entrance pupil. For example, in cameraapplications, the aperture stop of the camera may be an entrance pupilfor optical system 100 and the image surface 130 may be a surface of thecamera's image sensor, which may, for example, be a charge-coupleddevice (CCD) sensor or a complementary metal-oxide-semiconductor (CMOS)sensor.

Optical system 100 may be centered on folded optical axis 140 which maybe defined by an optical path of a central light ray transmitted throughthe image surface 130. The optical axis 140 is folded because theoptical path of the central light ray propagates in the minusz-direction in one segment of the optical path between the first andsecond optical stacks 110 and 120 and propagates in the plus z-directionon another segment of the optical path between the first and secondoptical stacks 110 and 120.

The first and second optical stacks 110 and 120 may have a substantiallysame shape or may have different shapes. Similarly, the first and secondoptical lenses 112 and 122 may have a substantially same shape or mayhave different shapes. Any one or more of the reflective polarizer, thefirst quarter wave retarder, the partial reflector, the first and secondmajor surfaces 114 and 116 of the first optical lens 112, and the firstand second major surfaces 124 and 126 of the second optical lens 120 mayhave a shape described by an aspheric polynomial sag equation. Thevarious surfaces or layers may have a same shape or may have differentshapes and may be described by the same or different aspheric polynomialsag equations. An aspheric polynomial sag equation may take the form

$\begin{matrix}{z = {\frac{{cr}^{2}}{1 + \left\lbrack {1 - {\left( {1 + k} \right)c^{2}r^{2}}} \right\rbrack^{1\text{/}2}} + {Dr}^{4} + {Er}^{6} + {Fr}^{8} + {Gr}^{10} + {Hr}^{12} + {Ir}^{14}}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

where c, k, D, E, F, G, H, and I are constants, z is the distance from avertex (e.g., distance s1 in FIG. 10) and r is a radial distance (e.g.,distance r1 in FIG. 10). The parameter k may be referred to as the conicconstant. Any of the optical systems of the present description mayinclude a reflective polarizer, one or more quarter wave retarders, apartial reflector and a plurality of major surfaces disposed between animage surface and a stop surface. Any one or more of the reflectivepolarizer, the one or more quarter wave retarders, the partialreflector, and the major surfaces may have shapes described by asphericpolynomial sag equations.

First optical stack 110 is disposed at a distance d1 from the imagesurface 130, second optical stack 120 is disposed at a distance d2 fromthe first optical stack 110 and at a distance d3 from the stop surface135. In some embodiments, the distances d1, d2 and/or d3 are adjustable.In some embodiments, the distance between image surface 130 and stopsurface 135 (d1+d2+d3) is fixed and d1 and/or d3 are adjustable. Thedistances d1, d2 and/or d3 may be user-adjustable by mounting one orboth of the first and second optical stacks 110 and 120 on a railproviding mechanical adjustment of the positions, for example.

The ability to adjust the positions of the first and second opticalstacks 110 and/or 120 relative to themselves or relative to the imageand/or stop surfaces 130 and 135 allows a dioptric correction providedby the optical system 100 to be adjustable. For example, moving thesecond optical stack 120 while keeping the remaining components fixedallows light rays emitted by the image surface 130 and transmittedthrough the stop surface to be adjustable from parallel at the stopsurface 135 to converging or diverging at the stop surface 135. In someembodiments, diopter values may be indicated on a mechanical adjustmentdevice, selectable physically through the use of a hard stop, detent orsimilar device, or electronically adjusted such as with a stepper motor,or motor or linear actuator used in conjunction with an electronicscale. In some embodiments, the image size on the display panelcomprising the image surface 130 may be changed based on the diopteradjustment. This can be done manually by the user or done automaticallythrough the adjustment mechanism. In other embodiments, one, two, threeor more optical lenses may be provided. In any embodiments in which apartial reflector is disposed on a surface of a first lens and areflective polarizer is disposed on a surface of a different secondlens, a changeable dioptric power may be provided, at least in part, byproviding an adjustable position of the first and/or second lens, and/orproviding an adjustable distance between the first and second lenses.

In some embodiments, one or both of the first and second optical lenses112 and 122 may be shaped to provide a diopter value and/or a cylinderpower (e.g., by molding the lenses with a toroidal surface, which may bedescribed as a surface having differing radii of curvature in twoorthogonal directions) so that the optical system 100 may provide adesired prescription correction for the user. An example of a toric lenshaving spherical and cylinder power in reflection and that can beutilized in the optical systems of the present description isillustrated in FIGS. 28A and 28B which are cross-sectional views of alens 2812 in a cross-section through an apex of the lens in a y-z planeand in an x-z plane, respectively. The radius of curvature is smallerthe y-z plane (FIG. 28A) than in the x-z plane (FIG. 28B). In someembodiments, cylinder power can be created by using thin plastic lensesthat can be flexed. Similarly, a prescription correction may be includedin any of the one, two, three or more lens optical systems describedherein by providing a suitable optical power to the lens or lenses. Insome embodiments, the optical system may be adapted to incorporate aprescription lens disposed between a display panel comprising the imagesurface and the other lenses of the optical system, which may notprovide dioptric correction, or the system may be adapted to incorporatea prescription lens disposed between the stop surface and the otherlenses of the optical system, which may not provide dioptric correction.

Another use for moveable optical lenses is to minimizevergence-accommodation mismatch in stereoscopic viewers. In manystereoscopic head-mounted displays, sense of depth is created by movingthe left eye and right eye images of certain objects closer together.The left and right eye converge in order to see the virtual image of theobject clearly and this is a cue that gives a perception of depth.However when the eyes view a real object that is near they not onlyconverge, but the lens of each eye focuses (also called accommodation)to bring the near object into focus on the retina. Because of disparitybetween the vergence cues present in stereoscopic viewers and the lackof accommodation in the eye to view the virtual image of near objects,many users of stereoscopic head-mounted displays can suffer from visualdiscomfort, eye-strain and/or nausea. By adjusting the positions of thefirst and second lenses, the virtual image distance can be adjusted tonear points so that the eyes focus to see the virtual image of objects.By combining vergence cues with accommodation cues, the positions of oneor more lenses in the optical system can be adjusted so thatvergence-accommodation mismatch can be reduced or substantially removed.

In some embodiments, a head-mounted display includes any of the opticalsystems of the present description and also may include an eye-trackingsystem. The eye-tracking system may be configured to detect where in thevirtual image that the user is looking and the optical system may beadapted to adjust the virtual image distance to match the depth of theobject as presented stereoscopically by adjusting the positions of oneor more lenses in the optical system.

In some embodiments, the first and/or second optical lenses 112 and 122may be shaped to have spherical and/or cylinder power in reflection orrefraction or both. This can be done, for example, by usingthermoforming molds and film insert molds having the desired shape.Cylinder power may be created by applying a stress to a rotationallysymmetric lens as it cools after an injection molding process, forexample. Alternatively, the lens may be curved (spherically orcylindrically or a combination) by post processing, diamond turning,grinding or polishing.

In some embodiments, one or both of the first and second optical lenses112 and 122 can be flexed in the optical system dynamically orstatically. An example of a static flexure is a set screw or set screwsor similar mechanism statically applying a compressive or tensile forceto the lens or lenses. In some embodiments, set screws could be providedin an annular manner to provide for astigmatism correction alongmultiple axes to account for all three types of astigmatism: with therule, against the rule and oblique astigmatism. This would provide foraccurate correction such as with eyeglass lenses which are typicallymade to address astigmatism in increments of 30 degrees or 15 degrees or10 degrees of obliquity. The pitch of the set screw can be related tocylinder power to provide a measure of correction based on turns orpartial turns of the screw. In some embodiments, piezo-electric,voice-coil, or stepper-motor actuators or other types of actuators canbe used to flex the lens or lenses (e.g., based on user input to thedevice such as entering a prescription).

In prescription lens terminology, a plano lens is a lens with norefractive optical power. In some embodiments, the first optical lens112 and/or the second optical lens 122 may be plano lenses having littleor no optical power in transmission, but may have optical power inreflection (for example, due to the overall curvature of the lenses).The curvature of the first and second major surfaces 114 and 116 of thefirst optical lens 112 may be the same or substantially the same, andthe curvature of the first and second major surfaces 124 and 126 of thesecond optical lens 122 may be the same or substantially the same. Thefirst and second optical lenses 112 and 122 may have the substantiallysame shape. In some embodiments, the first optical lens 112 and/or thesecond optical lens 122 may have optical power in transmission and mayalso have optical power in reflection.

Optical system 100 includes a reflective polarizer and a quarter waveretarder in second optical stack 120 and includes a partial reflector infirst optical stack 110. There are various possibilities of how thereflective polarizer, the quarter wave retarder and the partialreflector can be arranged in the optical stacks. FIG. 2 shows onepossible arrangement; other arrangements are described in FIGS. 3A-4C.

FIG. 2 is a schematic cross-sectional view of optical system 200including image surface 230, stop surface 235, a first optical stack 210disposed between the image surface 230 and the stop surface 235, asecond optical stack 220 is disposed between the first optical stack 210and the stop surface 235. Each of the first and second optical stacks210 and 220 are convex toward the image surface 230 along orthogonalfirst and second axes. An x-y-z coordinate system is provided in FIG. 2.The orthogonal first and second axes may be the x- and y-axes,respectively.

The first optical stack 210 includes a first optical lens 212 havingopposing first and second major surfaces 214 and 216 respectively. Thefirst optical stack 210 includes a partial reflector 217 disposed on thefirst major surface 214. The partial reflector 217 has an averageoptical reflectance of at least 30% in a desired or pre-determinedplurality of wavelengths and may have an average optical transmission ofat least 30% in the desired or pre-determined plurality of wavelengths,which may be any of the wavelength ranges described elsewhere herein.

The second optical stack includes a second optical lens 222 having firstand second major surfaces 224 and 226. The second optical stack 220includes a reflective polarizer 227 disposed on the second major surface226 and includes a quarter wave retarder 225 disposed on the reflectivepolarizer 227. Quarter wave retarder 225 may be a film laminated on thereflective polarizer 227 or may be a coating applied to the reflectivepolarizer 227. The optical system 200 may include one or more additionalretarders. For example, a second quarter wave retarder may be includedin first optical stack 210 and may be disposed on the second majorsurface 216. The first quarter wave retarder 225 and any additionalquarter wave retarders included in optical system 200 may be quarterwave retarders at at least one wavelength in the pre-determined ordesired plurality of wavelengths. The second optical stack 220 mayalternatively be described as including the second lens 222 and thereflective polarizer 227 disposed on the second lens 222 and the firstquarter wave retarder 225 may be regarded as a separate layer or coatingthat is disposed on the second optical stack 220 rather than beingincluded in the second optical stack 220. In this case, the firstquarter wave retarder 225 may be described as being disposed between thefirst optical stack 210 and the second optical stack 220. In someembodiments, the first quarter wave retarder 225 may not be attached tothe second optical stack 220, and in some embodiments, the first quarterwave retarder 225 is disposed between and spaced apart from the firstand second optical stacks 210 and 220. In still other embodiments, thefirst quarter wave retarder 225 may be disposed on the partial reflector217 and may be described as being included in the first optical stack210 or may be described as being disposed between the first and secondoptical stacks 210 and 220.

Light rays 237 and 238 are each transmitted through the image surface230 and the stop surface 235. Light rays 237 and 238 may each betransmitted from the image surface 230 to the stop surface 235 (inhead-mounted display applications, for example), or light rays 237 and238 may be transmitted from the stop surface 235, to the image surface230 (in camera applications, for example). Light ray 238 may be acentral light ray whose optical path defines a folded optical axis 240for optical system 200, which may be centered on the folded optical axis240. Folded optical axis 240 may correspond to folded optical axis 140.

In embodiments in which light ray 237 is transmitted from the imagesurface 230 to the stop surface 235, light ray 237 (and similarly forlight ray 238) is, in sequence, transmitted through image surface 230,transmitted through second major surface 216 (and any coatings or layersthereon), transmitted through first optical lens 212, transmittedthrough partial reflector 217, transmitted through the quarter waveretarder 225 disposed on the reflective polarizer 227, reflected fromreflective polarizer 227, transmitted back through quarter wave retarder225, reflected from partial reflector 217, transmitted through quarterwave retarder 225, transmitted through reflective polarizer 227,transmitted through second lens 222, and transmitted through stopsurface 235. Light ray 237 may be emitted from the image surface 230with a polarization state which is rotated to a first polarization stateupon passing through quarter wave retarder 225. This first polarizationstate may be a block state for the reflective polarizer 227. After lightray 237 passes through first quarter wave retarder 225, reflects frompartial reflector 217 and passes back through quarter wave retarder 225,its polarization state is a second polarization state substantiallyorthogonal to the first polarization state. Light ray 237 can thereforereflect from the reflective polarizer 227 the first time that it isincident on the reflective polarizer 227 and can be transmitted throughthe reflective polarizer 227 the second time that it is incident on thereflective polarizer 227.

Other light rays (not illustrated) reflect from the partial reflector217 when incident on the partial reflector 217 in the minus z-directionor are transmitted by the partial reflector 217 when incident on thepartial reflector 217 in the plus z-direction. These rays may exitoptical system 200.

In some embodiments, substantially any chief light ray that passesthrough the image surface 230 and the stop surface 235 is incident oneach of the first optical stack 210 and the second optical stack 220with an angle of incidence less than about 30 degrees, less than about25 degrees, or less than about 20 degrees, the first time or each timethat the chief light ray is incident on the first or second opticalstacks 210 or 220. In any of the optical systems of the presentdescription, substantially any chief light ray that passes through theimage and stop surfaces is incident on each of the reflective polarizerand the partial reflector with an angle of incidence less than about 30degrees, less than about 25 degrees, or less than about 20 degrees, thefirst time or each time that the chief light ray is incident on thereflective polarizer or the partial reflector. If a large majority(e.g., about 90 percent or more, or about 95 percent or more, or about98 percent or more) of all chief rays transmitted through the stop andimage surfaces satisfy a condition, it may be said that substantiallyany chief ray satisfies that condition.

Various factors can cause light to be partially transmitted through thereflective polarizer 227 the first time that light emitted by the imagesurface 230 is incident on the reflective polarizer 227. This can causeunwanted ghosting or image blurriness at the stop surface 235. Thesefactors can include performance degradation of the various polarizingcomponents during forming and unwanted birefringence in the opticalsystem 200. The effects of these factors can combine to degrade thecontrast ratio and efficiency of the optical system 200. The effects ofthese factors on the contrast ratio can be seen, for example, in FIG. 14which shows the contrast ratio at the stop surface 235 determined viaoptical modeling as a function of the percentage of the light having apolarization in the pass state when emitted by image surface 230 that isblocked by the reflective polarizer 227 when first incident on thereflective polarizer 227 after passing through first quarter waveretarder 225 and through a second quarter wave retarder (notillustrated) disposed on second major surface 216 of first lens 212.Such factors can be minimized by using relatively thin optical lenses,which can reduce unwanted birefringence in the lenses, for example, andusing thin optical films, which can reduce optical artifacts arisingfrom thermoforming optical films, for example. In some embodiments, thefirst and second optical lenses 212 and 222 each have a thickness lessthickness less than 7 mm, less than 5 mm, or less than 3 mm, and mayhave a thickness in a range of 1 mm to 5 mm, or 1 mm to 7 mm, forexample. In some embodiments, the reflective polarizer 227 may have athickness of less than 75 micrometers, less than 50 micrometers, or lessthan 30 micrometers. In some embodiments, the contrast ratio at the stopsurface 235 is at least 40, or at least 50, or at least 60, or at least80, or at least 100 over the field of view of the optical system 200. Ithas been found that the contrast ratio can be significantly higher ifthe reflective polarizer 227 is a thermoformed (so that it is curvedabout two orthogonal axes) multilayer optical film which was uniaxiallyoriented prior to thermoforming (e.g., APF), compared to using otherreflective polarizers curved about two orthogonal axes. Other reflectivepolarizers, such as non-uniaxially oriented multilayer polymeric filmreflective polarizers or wire grid polarizers), may also be used.

It has been found that suitably choosing the shapes of the various majorsurfaces (e.g., second major surface 226 and first major surface 214)that the optical system can provide distortion sufficiently low that theimage does not need to be pre-distorted. In some embodiments, an imagesource, which is adapted to emit an undistorted image, comprises theimage surface 230. The partial reflector 217 and the reflective polarize227 may have different shapes selected such that a distortion of theemitted undistorted image transmitted by the stop surface 235 is lessthan about 10%, or less than about 5%, or less than about 3%, of a fieldof view at the stop surface 235. The field of view at the stop surfacemay be greater than 80 degrees, greater than 90 degrees, or greater than100 degrees, for example.

FIGS. 3A-3C are cross-sectional views of portions of optical stacks 310a-310 c, any of which may correspond to first optical stack 110. Thoughnot shown in FIGS. 3A-3C, optical stacks 310 a-310 c may each be curvedabout two orthogonal axes. Each of the optical stacks 310 a-310 cincludes lens 312, which may correspond to optical lens 112, havingfirst and second major surfaces 314 and 316. Optical stack 310 aincludes quarter wave retarder 315, which may optionally be omitted,disposed on first major surface 314 and partial reflector 317 disposedon second major surface 316. Optical stack 310 b includes partialreflector 317 disposed on first major surface 314 and quarter waveretarder 315, which may optionally be omitted, disposed on partialreflector 317 opposite the optical lens 312. Optical stack 310 cincludes quarter wave retarder 315 disposed on second major surface 316and includes partial reflector 317 disposed on quarter wave retarder 315opposite lens 312.

FIGS. 4A-4C are cross-sectional views of portions of optical stacks 420a-420 c, any of which may correspond to second optical stack 120.Optical stacks 420 a-420 c may each be curved about two orthogonal axes.Each of the optical stacks 420 a-420 c includes lens 422 having firstand second major surfaces 424 and 426. Optical stack 420 a includesquarter wave retarder 425 disposed on first major surface 424 andreflective polarizer 427 disposed on second major surface 426. Opticalstack 420 b includes reflective polarizer 427 disposed on first majorsurface 424 and quarter wave retarder 425 disposed on reflectivepolarizer 427 opposite the lens 422 (as in FIG. 2). Optical stack 420 cincludes quarter wave retarder 425 disposed on second major surface 426and includes reflective polarizer 427 disposed on quarter wave retarder425 opposite lens 422.

An alternate embodiment is shown in FIG. 5, which is a schematiccross-sectional view of optical system 500 including image surface 530,stop surface 535, and integral optical stack 510 including optical lens512 having first and second major surfaces 514 and 516. The first and/orsecond major surfaces 514 and 516 may have one or more layers orcoatings disposed thereon. The integral optical stack 510 also includesa partial reflector, a multilayer reflective polarizer and a firstquarter wave retarder. These various layers or components may bedisposed on one or more of first and second major surfaces 514 and 516.For example, in some embodiments the partial reflector may be disposedon the first major surface 514, the first quarter wave retarder may bedisposed on the partial reflector and the reflective polarizer may bedisposed on the first quarter wave retarder. In some embodiments, asecond quarter wave retarder may be disposed on second major surface516. In some embodiments, the reflective polarizer is disposed on secondmajor surface 516, the quarter wave retarder is disposed on thereflective polarizer and the partial reflector is disposed on quarterwave retarder. In some embodiments, a second quarter wave retarder isdisposed on the partial reflector. In some embodiments, the reflectivepolarizer is disposed on first major surface 514 and the first quarterwave retarder is disposed on second major surface 516 with the partialreflector and an optional second quarter wave retarder disposed on thefirst quarter wave retarder. In some embodiments, the first quarter waveretarder is disposed on first major surface 514 with the reflectivepolarizer disposed on the first quarter wave retarder and the partialreflector is disposed on the second major surface 516 with an optionalsecond quarter wave retarder disposed on the partial reflector.

The image surface 530 has a first maximum lateral dimension and the stopsurface 535 has a second maximum lateral dimension. In some embodiments,the first maximum lateral dimension divided by the second maximumlateral dimension may be at least 2, at least 3, at least 4, or at least5. The image surface 530 and/or the stop surface 635 may besubstantially planar or may be curved about one or more axes.

The partial reflector has an average optical reflectance of at least 30%in a desired or pre-determined plurality of wavelengths and may have anaverage optical transmission of at least 30% in the desired orpre-determined plurality of wavelengths, which may be any of thewavelength ranges described elsewhere herein. The quarter waveretarder(s) included in optical system 500 may be quarter wave retardersat at least one wavelength in the pre-determined or desired plurality ofwavelengths. The multilayer reflective polarizer substantially transmitslight having a first polarization state (e.g., linearly polarized in afirst direction) and substantially reflects light having an orthogonalsecond polarization state (e.g., linear polarized in a second directionorthogonal to the first direction). As described further elsewhereherein, the multilayer reflective polarizer may be a polymericmultilayer reflective polarizer (e.g., APF) or may be a wire gridpolarizer, for example.

Optical system 500 may be centered on folded optical axis 540 which maybe defined by the optical path of a central light ray transmittedthrough image surface 530.

It has been found that using a single integrated optical stack, such asintegrated optical stack 510, can provide a high field of view in acompact system. Light ray 537, which is transmitted through an outeredge of image surface 530, is a chief ray that intersects stop surface535 at the folded optical axis 540 with a view angle of θ, which may beat least 40 degrees, at least 45 degrees, or at least 50 degrees, forexample. The field of view at the stop surface 535 is 2θ, which may beat least 80 degrees, at least 90 degrees, or at least 100 degrees, forexample.

FIG. 6 is a schematic cross-sectional view of optical system 600, whichmay correspond to optical system 500, including image surface 630, stopsurface 635, integral optical stack 610 including optical lens 612having first and second major surfaces 614 and 616. First quarter waveretarder 625 is disposed on first major surface 614 of optical lens 612and reflective polarizer 627 is disposed on first quarter wave retarder625 opposite optical lens 612. Partial reflector 617 is disposed onsecond major surface 616 of optical lens 612 and second quarter waveretarder 615 is disposed on partial reflector 617 opposite optical lens612. Optical system 600 may be centered on folded optical axis 640 whichmay be defined by an optical path of a central light ray transmittedthrough the image surface 630.

Integral optical stack 610 can be made by first forming reflectivepolarizer 627 with first quarter wave retarder 625 coated or laminatedto reflective polarizer 627 and then thermoforming the resulting filminto a desired shape. As described further elsewhere herein, thethermoforming tool may have a shape different than the desired shape sothat the film obtains the desired shape after cooling. Partial reflector617 and second quarter wave retarder 615 may be prepared by coating aquarter wave retarder onto a partial reflector film, by coating apartial reflector coating onto a quarter wave retarder film, bylaminating a partial reflector film and a quarter wave retarder filmtogether, or by first forming lens 612 (which may be formed on a filmthat includes reflective polarizer 627 and first quarter wave retarder625) in a film insert molding process and then coating the partialreflector 617 on the second major surface 616 and coating the quarterwave retarder 615 on the partial reflector 617. In some embodiments, afirst film including reflective polarizer 627 and first quarter waveretarder 625 is provided and a second film including partial reflector617 and second quarter wave retarder 615 is provided and then integraloptical stack 610 is formed by injection molding lens 612 between thefirst and second thermoformed films in a film insert molding process.The first and second films may be thermoformed prior to the injectionmolding step. Other optical stacks of the present description may bemade similarly by thermoforming an optical film, which may be a coatedfilm or a laminate, and using a film insert molding process to make theoptical stack. A second film may be included in the film insert moldingprocess so that the lens formed in the molding process is disposedbetween the films.

Image source 631 includes the image surface 630 and stop surface 635 isan exit pupil for optical system 600. Image source 631 may be a displaypanel, for example. In other embodiments, a display panel is not presentand, instead, image surface 630 is an aperture adapted to receive lightreflected from objects external to optical system 600. A second opticalsystem 633 having an entrance pupil 634 is disposed proximate opticalsystem 600 with stop surface 635 overlapping entrance pupil 634. Thesecond optical system 633 may be a camera, for example, adapted torecord images transmitted through image surface 637. In someembodiments, the second optical system is a viewer's eye and entrancepupil 634 is the pupil of the viewer's eye. In such embodiments, theoptical system 600 may be adapted for use in a head-mounted display.

The partial reflector 617 has an average optical reflectance of at least30% in a desired or pre-determined plurality of wavelengths and may havean average optical transmission of at least 30% in the desired orpre-determined plurality of wavelengths, which may be any of thewavelength ranges described elsewhere herein. The first quarter waveretarder 625 and any additional quarter wave retarders included inoptical system 600 may be quarter wave retarders at at least onewavelength in the pre-determined or desired plurality of wavelengths.The multilayer reflective polarizer 627 substantially transmits lighthaving a first polarization state (e.g., linearly polarized in a firstdirection) and substantially reflects light having an orthogonal secondpolarization state (e.g., linear polarized in a second directionorthogonal to the first direction). As described further elsewhereherein, the multilayer reflective polarizer 627 may be a polymericmultilayer reflective polarizer (e.g., APF) or may be a wire gridpolarizer, for example.

Light ray 637 is emitted from the image source 631 and transmittedthrough the image surface 630 and the stop surface 635. Light ray 637 istransmitted through second quarter wave retarder 615 and partialreflector 617 into and through lens 612. Other light rays (notillustrated) reflect from partial reflector 617 after passing throughsecond quarter wave retarder 615 and are lost from the optical system600. After making a first pass through lens 612, the light ray passesthrough first quarter wave retarder 625 and reflects from reflectivepolarizer 627. Image source 631 may be adapted to emit light having apolarization along the pass axis for reflective polarizer 627 so thatafter passing through both second quarter wave retarder 615 and firstquarter wave retarder 625 it is polarized along the block axis for thereflective polarizer 627 and therefore reflects from the reflectivepolarizer 627 when it is first incident on it. In some embodiments, alinear polarizer is included between the display panel 631 and thesecond quarter wave retarder 617 so that light incident on secondquarter wave retarder 615 has the desired polarization. After light ray637 reflects from reflective polarizer 627, it passes back through firstquarter wave retarder 625 and lens 612 and is then reflected frompartial reflector 617 (other light rays not illustrated are transmittedthrough partial reflector 617) back through lens 612 and is then againincident on the reflective polarizer 627. After passing through firstquarter wave retarder 625, reflecting from partial reflector 617 andpassing back through first quarter wave retarder 625, light ray 637 hasa polarization along the pass axis for reflective polarizer 627. Lightray 637 is therefore transmitted through reflective polarizer 627 and isthen transmitted through stop surface 635 into second optical system633.

In alternate embodiments, the integrated optical stack 610 is replacedwith first and second optical stacks as in FIGS. 1-2 or is replaced withfirst, second, and third optical stacks as in FIG. 8.

FIG. 7 is a schematic cross-sectional view of optical system 700, whichmay correspond to optical system 500, including image surface 730, stopsurface 735, and integral optical stack 710 including optical lens 712having first and second major surfaces 714 and 716. First quarter waveretarder 725 is disposed on optical lens 712 and reflective polarizer727 is disposed on first quarter wave retarder 725. Partial reflector717 is disposed on second major surface 716. Optical system 700 may becentered on folded optical axis 740 which may be defined by an opticalpath of a central light ray transmitted through the image surface 730.

Image recorder 732 includes the image surface 730, and stop surface 735is an entrance pupil for optical system 700. The stop surface may be anaperture stop of a camera, for example. Image recorder 732 may be a CCDor a CMOS device, for example. Optical system 700 may be a camera or acomponent of a camera and may be disposed in a cell phone, for example.

The partial reflector 717 has an average optical reflectance of at least30% in a desired or pre-determined plurality of wavelengths and may havean average optical transmission of at least 30% in the desired orpre-determined plurality of wavelengths, which may be any of thewavelength ranges described elsewhere herein. The first quarter waveretarder 725 and any additional quarter wave retarders included inoptical system 700 may be quarter wave retarders at at least onewavelength in the pre-determined or desired plurality of wavelengths.The multilayer reflective polarizer 727 substantially transmits lighthaving a first polarization state (e.g., linearly polarized in a firstdirection) and substantially reflects light having an orthogonal secondpolarization state (e.g., linear polarized in a second directionorthogonal to the first direction). As described further elsewhereherein, the multilayer reflective polarizer 727 may be a polymericmultilayer reflective polarizer (e.g., APF) or may be a wire gridpolarizer, for example.

Light ray 737 is transmitted through the stop surface 735 andtransmitted through the image surface 730 into image recorder 732. Lightray 737 is, in sequence, transmitted through reflective polarizer 727(other light rays not illustrated may be reflected by reflectivepolarizer 727), transmitted through quarter wave retarder 725 andoptical lens 712, reflected from partial reflector 717 and transmittedback through lens 712 and quarter wave retarder, reflected fromreflective polarizer 727 and transmitted through the quarter waveretarder 725, the lens 712 and the partial reflector 717. The light ray737 is then transmitted through image surface 730 into image recorder732.

Any of the integral optical stacks 510, 610, and 710 may optionallyinclude a second lens adjacent the first lens with one or more of thereflective polarizer, the quarter wave retarder and the partialreflector disposed between the two lenses. The two lenses may belaminated together using optically clear adhesive. FIG. 26 is aschematic cross-sectional view of integral optical stack 2610, which maybe used in place of any of integral optical stacks 510, 610 and 710 inthe optical systems 500, 600, and 700, respectively. Integral opticalstack 2610 includes first lens 2612, second lens 2622 and a quarter waveretarder 2625 disposed between the first and second lens 2612 and 2622.The quarter wave retarder 2625 may be coated onto a major surface of thesecond lens 2622, for example, and an optically clear adhesive may beused to attach the quarter wave retarder 2625 to the first lens 2612.Alternatively, the quarter wave retarder 2625 could be coated onto amajor surface of the first lens 2612 and an optically clear adhesivecould be used to attach the quarter wave retarder 2625 to the secondoptical lens 2622. In other embodiments, the quarter wave retarder 2625may be a separate film that is laminated to both of the first and secondlenses 2612 and 2622. Optical stack includes reflective polarizer 2627disposed on a major surface of second lens 2622 opposite first lens 2612and includes a partial reflector 2617 disposed on a major surface of thefirst lens 2612 opposite the second lens 2622. The partial reflector2617, the quarter wave retarder 2625, and the reflective polarizer 2627may correspond to any of the partial reflectors, the quarter waveretarders and the reflective polarizers, respectively describedelsewhere herein.

The first and second lenses 2612 and 2622 may be formed from first andsecond materials, respectively, that may be the same or different. Forexample, the material of the lenses 2612 2622 may be a same glass, maybe different glasses, may be the same polymer, may be differentpolymers, or one may be a glass and the other may be a polymer. Thematerial chosen for the lenses will typically exhibit some degree ofdispersion (dependence of the refractive index on wavelength). In somecases, the effects of dispersion can be reduced by choosing differentmaterials for the different lenses such that the dispersion in one lenscompensates or partially compensates for the dispersion in the otherlens. The Abbe number of a material is can be used to quantify thedispersion of a material. The Abbe number is given as(n_(D)−1)/(n_(F)−n_(C)) where n_(D) is the refractive index at 589.3 nm,n_(F) is the refractive index of 486.1 nm and n_(C) is the refractiveindex at 656.3 nm. In some embodiments, the first and second lenses 2612and 2622 have differing Abbe numbers. In some embodiments, a differencein the Abbe numbers of the first and second lenses 2612 and 2622 is in arange of 5 to 50. In some embodiments, one of the first and secondlenses 2612 and 2622 has an Abbe number greater than 45, or greater than50, and the other of the first and second lenses 2612 and 2622 has anAbbe number less than 45, or less than 40. This can be achieved, forexample, by using a glass for one of the lenses, and using a polymer forthe other of the lenses.

Optical system of the present description may include one, two, three ormore lenses disposed between an image surface and a stop surface. Insome embodiments a plurality of major surfaces is disposed between theimage surface and the stop surface with each major surface convex towardthe image surface along the first and second axes. In some embodiments,at least six such major surfaces are included. In some embodiments, atleast six different major surfaces have at least six differentconvexities. Including three or more lenses in an optical system may beuseful when a small panel having a high resolution is utilized, forexample, since having three or more lenses provides six or more majorsurfaces whose shape can be selected to give desired optical properties(e.g., large field of view) at the stop surface of the optical system.

FIG. 8 is a schematic cross-sectional view of optical system 800including first optical lens 812 having first and second major surfaces814 and 816, second optical lens 822 having first and second majorsurfaces 824 and 826, and third optical lens 862 having first and secondmajor surfaces 864 and 866, each disposed between image surface 830 andstop surface 835. The image surface 830 and/or the stop surface 835 maybe substantially planar or may be curved. Any of the first and secondoptical surfaces may include one or more layers or coatings thereon, asdescribed further elsewhere herein. Optical system 800 includes apartial reflector, a multilayer reflective polarizer and a first quarterwave retarder disposed between the image surface 830 and the stopsurface 835. Each of these components may be disposed on one of themajor surfaces 864, 866, 824, 826, 814 and 816. In some embodiments, thepartial reflector is disposed on the first major surface 824 of thesecond optical lens 822. In some embodiments, the multilayer reflectivepolarizer is disposed on the first major surface 864 or on the secondmajor surface 866 of the third optical lens 862. In some embodiments,the first quarter wave retarder is disposed on the multilayer reflectivepolarizer. In some embodiments, the first quarter wave retarder isdisposed on the first major surface 864 of the third optical lens 862and the multilayer reflective polarizer is disposed on the multilayerreflective polarizer. In some embodiments, a second quarter waveretarder is included in optical system 800. The second quarter waveretarder may be disposed on the second major surface 826 of the secondoptical lens 822 or may be disposed on one of the first and second majorsurfaces 814 and 816 of the first optical lens 812.

The image surface 830 has a first maximum lateral dimension and the stopsurface 835 has a second maximum lateral dimension. In some embodiments,the first maximum lateral dimension divided by the second maximumlateral dimension may be at least 2, at least 3, at least 4, or at least5.

Optical system 800 may be centered on folded optical axis 840 which maybe defined by an optical path of a central light ray transmitted throughthe image surface 830.

The partial reflector may have an average optical reflectance of atleast 30% in a pre-determined or desired plurality of wavelengths andmay have an average optical transmittance of a least 30% in thepre-determined or desired plurality of wavelengths, which may be any ofthe wavelength ranges described elsewhere herein. The first quarter waveretarder and any additional quarter wave retarders included in opticalsystem 800 may be quarter wave retarders at at least one wavelength inthe pre-determined or desired plurality of wavelengths. The multilayerreflective polarizer may substantially transmit light having a firstpolarization state, which may be a linear polarization state, andsubstantially reflect light having an orthogonal second polarizationstate, which may be an orthogonal linear polarization state. Asdescribed further elsewhere herein, the multilayer reflective polarizermay be a polymeric multilayer reflective polarizer (e.g., APF) or may bea wire grid polarizer, for example.

In some embodiments, each of the major surfaces major surfaces 864, 866,824, 826, 814 and 816 have a convexity different from the convexity ofeach of the remaining major surfaces. In other words, the major surfacesmajor surfaces 864, 866, 824, 826, 814 and 816 may have six differentconvexities.

An image source may comprise the image surface 830 and the stop surface835 may be an exit pupil, which may be adapted to overlap an entrancepupil of a second optical system. The entrance pupil of the secondoptical system may be an entrance pupil of a viewer's eye, for example.Alternatively, an image recorder may comprise the image surface 830 andthe stop surface 835 may be an entrance pupil.

FIG. 9 is a schematic cross-sectional view of optical system 900including first and second optical lenses 912 and 922 disposed betweenimage surface 930 and stop surface 935. Optical system 900 maycorrespond to optical systems 100 or 200. As described further elsewhereherein, image surface 930 may be a surface of an image source such as adisplay panel and stop surface 935 may be an exit pupil. First lens 912includes first and second major surfaces 914 and 916. First majorsurface 914 includes one or more layers 914 disposed thereon. Secondmajor surface 916 may also include one or more layers disposed thereon.Second lens 922 includes first and second major surfaces 924 and 926.Second major surface 926 includes one or more layers 945 disposedthereon. In some embodiments, first major surface 924 may also includeone or more layers disposed thereon. In the illustrated embodiment, oneor more layers 945 includes a reflective polarizer disposed on secondmajor surface 926 and includes a first quarter wave retarder disposed onthe reflective polarizer. In the illustrated embodiment, one or morelayers 943 includes a partial reflector. In other embodiments, asdescribed further elsewhere herein, the reflective polarizer, the firstquarter wave retarder, and the partial reflector are disposed ondifferent surfaces of first and second lenses 912 and 922.

Chief light ray 937 and envelope rays 939 a and 939 b are transmittedthrough image surface 930 and through stop surface 935. Chief light ray937 and envelope rays 939 a and 939 b propagate from image surface 930and through stop surface 935. In other embodiments, the directions ofthe light paths are reversed and image surface 930 may be a surface ofan image recorder. Envelope rays 939 a and 939 b intersect the stopsurface 935 at boundaries of the stop surface 935 while chief ray 937intersect the stop surface 935 at optical axis 940, which may be definedby an optical path of a central light ray transmitted through the imagesurface 930.

Chief light ray 937 is incident on the stop surface 935 at optical axis940 at an incidence angle θ. Twice the maximum incidence angle on thestop surface 935 of a chief ray incident on the stop surface 935 alongthe optical axis 940 is the field of view of optical system 900. In someembodiments, optical system 900 has a low chromatic aberration. Forexample, in some embodiments, substantially any chief light ray havingat least first and second wavelengths at least 150 nm apart in a visiblewavelength range (e.g., first and second wavelengths of 486 nm and 656nm, respectively) and that is transmitted through the image surface 930and the stop surface 935 has a color separation distance at the stopsurface 935 of less than 1.5 percent, or less than 1.2 percent, of afield of view at the stop surface 935. In some embodiments,substantially any chief light ray having at least first and secondwavelengths at least 150 nm apart in a visible wavelength range and thatis transmitted through the image surface 930 and the stop surface 935has a color separation distance at the stop surface 935 of less than 20arc minutes, or less than 10 arc minutes.

Additional optical systems of the present description are illustrated inFIGS. 18-23. FIG. 18 is a cross-sectional view of optical system 1800including an optical stack 1810, an image surface 1830 and a stopsurface 1835. Image surface 1830 is a surface of panel 1889. Opticalstack 1810 includes a lens 1812, a reflective polarizer 1827 disposed onthe major surface of lens 1812 facing stop surface 1835, and a partialreflector 1817 disposed on the major surface of lens 1812 facing theimage surface 1830. A quarter wave retarder is included in optical stack1810 between the reflective polarizer and the lens 1812 or between thepartial reflector and the lens 1812. Lens 1812 is convex toward imagesurface 1830 about orthogonal axes (e.g., x- and y-axes). Three bundlesof light rays at three locations on the image surface 1830 areillustrated. The light rays in each bundle are substantially parallel atthe stop surface 1835. The light rays may travel predominately from thestop surface 1835 to the image surface 1830 (e.g., in cameraapplications), or may travel predominately from the image surface 1830to the stop surface 1835 (e.g., in display applications). Panel 1889 maybe a display panel or may be an image recording panel. The reflectionaperture of a reflective polarizer may be substantially an entire areaof the reflective polarizer or may include the entire area of thereflective polarizer except for a portion near a boundary of thereflective polarizer. In the illustrated embodiment, the reflectivepolarizer 1827 has a reflection aperture 1814 which substantiallycoincides with the entire area of the major surface of lens 1812 facingstop surface 1835.

FIG. 19 is a cross-sectional view of optical system 1900 including afirst optical stack 1910, a second optical stack 1920, an image surface1930 and a stop surface 1935. Image surface 1930 is a surface of panel1989. First optical stack 1910 includes a lens 1912 and a partialreflector disposed on the major surface of lens 1912 facing stop surface1935. Second optical stack 1920 includes a lens 1922 and includes areflective polarizer disposed on the major surface of lens 1922 facingthe image surface 1930. A quarter wave retarder is included eitherdisposed on the reflective polarizer facing the partial reflector ordisposed on the partial reflector facing the reflective polarize. Lens1912 and lens 1922 are convex toward image surface 1930 about orthogonalaxes (e.g., x- and y-axes). Three bundles of light rays at threelocations on the image surface 1930 are illustrated. The light rays ineach bundle are substantially parallel at the stop surface 1935. Thelight rays may travel predominately from the stop surface 1935 to theimage surface 1930 (e.g., in camera applications), or may travelpredominately from the image surface 1930 to the stop surface 1935(e.g., in display applications). Panel 1989 may be a display panel ormay be an image recording panel.

FIG. 20 is a cross-sectional view of optical system 2000 including anoptical stack 2010 having a first lens 2012, a second lens 2022, animage surface 2030 and a stop surface 2035. Image surface 2030 is asurface of panel 2089. Optical stack 2010 includes a reflectivepolarizer disposed on the major surface of first lens 2012 facing stopsurface 2035 and includes a partial reflector disposed on the majorsurface of first lens 2012 facing the image surface 2030. A quarter waveretarder is included in optical stack 2010 between the reflectivepolarizer and the first lens 2012 or between the partial reflector andthe first lens 2012. The reflective polarizer and the partial reflectorare convex toward image surface 2030 about orthogonal axes (e.g., x- andy-axes). Three bundles of light rays at three locations on the imagesurface 2030 are illustrated. The light rays in each bundle aresubstantially parallel at the stop surface 2035. The light rays maytravel predominately from the stop surface 2035 to the image surface2030 (e.g., in camera applications), or may travel predominately fromthe image surface 2030 to the stop surface 2035 (e.g., in displayapplications). Panel 2089 may be a display panel or may be an imagerecording panel.

FIG. 21 is a cross-sectional view of optical system 2100 including afirst optical stack 2110, a second optical stack 2120, an image surface2130 and a stop surface 2135. Image surface 2130 is a surface of panel2189. First optical stack 2110 includes a lens 2122 and a partialreflector disposed on the major surface of lens 2112 facing imagesurface 2130. Second optical stack 2120 includes a lens 2122 andincludes a reflective polarizer disposed on the major surface of lens2122 facing the image surface 2130. A quarter wave retarder is includedeither in optical system 2100 disposed on the reflective polarizerfacing the partial reflector, or disposed on the partial reflectorfacing the reflective polarizer, or disposed on the major surface oflens 2112 facing the stop surface 2135. The reflective polarizer isconvex toward image surface 2130 about orthogonal axes (e.g., x- andy-axes). The partial reflector may be substantially flat. Three bundlesof light rays at three locations on the image surface 2130 areillustrated. The light rays in each bundle are substantially parallel atthe stop surface 2135. The light rays may travel predominately from thestop surface 2135 to the image surface 2130 (e.g., in cameraapplications), or may travel predominately from the image surface 2130to the stop surface 2135 (e.g., in display applications). Panel 2189 maybe a display panel or may be an image recording panel.

FIG. 22 is a cross-sectional view of optical system 2200 including afirst lens 2212, an optical stack 2220 having a second lens 2222, animage surface 2230 and a stop surface 2235. Optical stack 2220 includesa partial reflector disposed on the major surface of lens 2222 facingimage surface 2230 and includes a reflective polarizer disposed on themajor surface of lens 2222 facing the stop surface 2235. A quarter waveretarder is included either in optical system 2200 disposed on thereflective polarizer facing the partial reflector, or disposed on thepartial reflector facing the reflective polarizer. The reflectivepolarizer is convex toward stop surface 2235 about orthogonal axes(e.g., x- and y-axes). The partial reflector may be substantially flator may be convex or concave. Three bundles of light rays at threelocations on the image surface 2230 are illustrated. The light rays ineach bundle are substantially parallel at the stop surface 2235. Thelight rays may travel predominately from the stop surface 2235 to theimage surface 2230 (e.g., in camera applications), or may travelpredominately from the image surface 2230 to the stop surface 2235(e.g., in display applications).

FIG. 23 is a cross-sectional view of optical system 2300 including afirst lens 2312, an optical stack 2320 including a second lens 2322, anoptical stack 2360 including a third lens 2362, an image surface 2330and a stop surface 2335. Optical stack 2320 includes a partial reflectordisposed on the major surface of second lens 2322 facing stop surface2335 and includes a reflective polarizer disposed on the major surfaceof third lens 2362 facing the image surface 2330. A quarter waveretarder is included either in optical system 2300 disposed on thereflective polarizer facing the partial reflector, or disposed on thepartial reflector facing the reflective polarizer. The reflectivepolarizer and the partial reflector are each convex toward image surface2330 about orthogonal axes (e.g., x- and y-axes). Three bundles of lightrays at three locations on the image surface 2330 are illustrated. Thelight rays in each bundle are substantially parallel at the stop surface2335. The light rays may travel predominately from the stop surface 2335to the image surface 2330 (e.g., in camera applications), or may travelpredominately from the image surface 2330 to the stop surface 2335(e.g., in display applications).

FIG. 10 is a cross-sectional view of reflective polarizer 1027 which hasapex 1057 and is curved about two orthogonal axes (e.g., the x-axis andthe y-axis). The reflective polarizer 1027 has at least one firstlocation 1052 having a radial distance r1 from an optical axis 1040passing through the apex 1057, and a displacement s1 from a plane 1057(parallel to the x-y plane) perpendicular to the optical axis 1040 atthe apex 1057. The ratio s1/r1 is at least 0.1, or at least 0.2, and maybe less than 0.8 or less than 0.6. For example, in some embodiments,s1/r1 is in a range of 0.2 to 0.8 or in a range of 0.3 to 0.6. Thereflective polarizer 1027 has at least one second location 1054 having aradial distance r2 from the optical axis 1040 and a displacement s2 fromthe plane 1047. In some embodiments, s2/r2 is at least 0.3, and may beless than 0.8. The reflective polarizer 1027 has a diameter D and amaximum sag Sm.

In some embodiments, the reflective polarizer is rotationally symmetricor substantially rotationally symmetric about optical axis 1040. A filmor component may be said to be substantially rotationally symmetric ifthe azimuthal variation in the shape of the film or component is nogreater than about 10 percent. In the embodiments in FIGS. 10 and 11,azimuthal variation refers to variation with the azimuthal angularcoordinate about the optical axis 1040 or 1140 through the apex 1057 or1157. In some embodiments, the azimuthal variation in s1/r1 is less than10 percent, or less than 8 percent, or less than 6 percent, or less than4 percent, or less than 2 percent, or less than 1 percent, or even lessthan 0.5 percent. The one or more locations 1052 may be a ring oflocations having a common radial distance r1 from the optical axis 1040,and similarly the one or more locations 1054 may be a ring of locationshaving a common radial distance r2 from the optical axis 1040. A filmmay be said to be rotationally symmetric if the azimuthal variation inthe shape of the film is sufficiently small that the film can be moldedinto a rotationally symmetric lens without wrinkling the film. A film orcomponent may be said to be rotationally symmetric if the azimuthalvariation in the shape of the film or component is no greater than about1 percent, or no greater than about 0.5 percent. The coordinates s1 andr1 define an area A1 of the reflective polarizer 1027 having a radialposition from the optical axis 1040 of no more than r1 or having adistance along the optical axis from the apex 1057 of no more than s1.

FIG. 11 is a front view of reflective polarizer 1127, which maycorrespond to reflective polarizer 1027. Reflective polarizer 1127 iscurved about two orthogonal axes (e.g., the x- and y-axes) and has anapex 1157 and an optical axis 1140 (parallel to z-axis) passing throughapex 1157. The reflective polarizer 1127 may be a polymeric multilayerreflective polarizer and may have at least one layer that issubstantially uniaxailly oriented at the apex 1157. For example, theorientation of the at least one layer may be in the y-direction asindicated by the arrow at apex 1157. This direction may also be a blockdirection for the reflective polarizer 1127 and the orthogonal direction(x-direction) may be transmission axis for the reflective polarizer.Reflective polarizer 1127 also includes at least one layer that issubstantially optically biaxial at at least one first location 1153 onthe at least one layer away from the optical axis 1140 and substantiallyoptically uniaxial at at least one second location 1152 away from theoptical axis.

A polymeric multilayer optical film may be thermoformed to providereflective polarizer 1127. The optical film may initially have at leastone layer uniaxially oriented with a block axis along the y-direction.During thermoforming the optical film is stretched to conform to theshape of a thermoform tool. The optical film is stretched since thedesired shape is curved about two orthogonal axes. In contrast to this,an optical film would not need to be stretched to conform to a shapecurved about only one axis. The process of thermoforming can leave theoptical film substantially uniaxially oriented at second location 1152(since the film is stretched along the orientation direction at thislocation during thermoforming), but result in biaxial orientation atfirst location 1153 due to the stretching of the optical film as it isthermoformed. The block axes at first and second locations 1153 and 1152are indicated by the arrows at those locations. The block axis isshifted by a degrees at the first location 1153. The transmission axismay orthogonal to the block axis and may also be shifted by a degrees atthe first location 1153. In some embodiments, a maximum variation of atransmission axis (or of a block axis) of the reflective polarizer 1127is less than about 5 degrees, or less than about 3 degrees, or less thanabout 2 degrees, or less than about 1.5 degrees, or less than about 1degree over the entire area of the reflective polarizer or over an areaof the reflective polarizer defined by s1 and r1, or over a reflectionaperture of the reflective polarizer, where s1 and s2 are as describedfor reflective polarizer 1027. The reflection aperture refers to theportion of the reflective polarizer that is utilized by the opticalsystem in reflection. The reflection aperture may be substantially theentire area of the reflective polarizer or may exclude a portion of thereflective polarizer near a boundary of the reflective polarizer. Themaximum variation of the transmission axis may be determined as themaximum angular difference between the transmission axis and a fixeddirection (e.g., the x-direction in FIG. 11) minus the minimum angulardifference between the transmission axis and a fixed direction.

Any of the reflective polarizers used in any of the optical systemsdescribed herein may be linear reflective polarizers which may beadapted to reflect light having a first linear polarization state andtransmit light having a second linear polarization state orthogonal tothe first linear polarization state.

Any of the reflective polarizers used in any of the optical systems ofthe present description may be a thermoformed reflective polarizer whichmay be a thermoformed polymeric multilayer optical film. The polymericmultilayer optical film may include a plurality of alternating first andsecond polymeric layers. This is illustrated in FIG. 12 which is a sideview of reflective polarizer 1227 including alternating first polymericlayers 1272 and second polymeric layers 1274. The out-of-plane(thickness) z-direction and orthogonal in-plane x- and y-directions areindicated in the figure. Suitable polymeric multilayer reflectivepolarizers are described, for example, in U.S. Pat. No. 5,882,774 (Jonzaet al.), and U.S. Pat. No. 6,609,795 (Weber et al.).

In some embodiments, at least one layer of the first and secondpolymeric layers 1272 and 1274 may be substantially uniaxially orientedat some locations in the layer. In some embodiments, the multilayeroptical film, prior to thermoforming, has at least one layer havingindices of refraction in a length direction (e.g., x-direction) and athickness direction (e.g., z-direction) that are substantially the same,but substantially different from an index of refraction in a widthdirection (e.g., y-direction). In some embodiments, the multilayeroptical film, prior to thermoforming, is a substantially uniaxiallydrawn film and has a degree of uniaxial character U of at least 0.7, orat least 0.8, or at least 0.85, where U=(1/MDDR−1)/(TDDR^(1/2)−1) withMDDR defined as the machine direction draw ratio and TDDR defined as thetransverse direction draw ratio. Such uniaxially oriented multilayeroptical films are described in U.S. Pat. No. 2010/0254002 (Merrill etal.), which is hereby incorporate herein by reference to the extent thatit does not contradict the present description. In other embodiments,the multilayer optical film, prior to thermoforming, is notsubstantially uniaxially drawn.

Uniaxially oriented multilayer reflective polarizers include APF(Advanced Polarizing Film, available from 3M Company). APF includes aplurality of alternating first and second polymeric layers with thefirst polymeric layers having indices of refraction in a lengthdirection (e.g., x-direction) and a thickness direction (e.g.,z-direction) that are substantially the same, but substantiallydifferent from an index of refraction in a width direction (e.g.,y-direction). For example, the absolute value of the difference in therefractive indices in the x- and z-directions may be less than 0.02 orless than 0.01, and the absolute value of the difference in therefractive indices in the x- and y-directions may be greater than 0.05,or greater than 0.10. APF is a linear reflective polarizer with a blockaxis along the width direction and a pass axis along the lengthdirection. Any of the reflective polarizers used in any of the opticalsystems of the present description may be a thermoformed APF. Unlessspecified differently, refractive index refers to the refractive indexat a wavelength of 550 nm.

A reflective polarizer which is not uniaxially oriented is DBEF (DualBrightness Enhancement Film available from 3M Company, St. Paul, Minn.).DBEF may have first layers with refractive indices in the width, lengthand thickness directions of about 1.80, 1.62 and 1.50, respectively,while APF may have first layers with refractive indices in the width,length and thickness directions of about 1.80, 1.56 and 1.56,respectively. Both APF and DBEF may have substantially isotropic secondlayers. In some embodiments, the optical system may use DBEF as thereflective polarizer, and in some embodiments, the optical system mayuse APF as the reflective polarizer. In still other embodiments,multilayer polymeric reflective polarizer films other than DBEF or APFmay be used. APF has unexpectedly been found to offer improvements overDBEF when thermoformed into a shape convex about two orthogonal axes.Such improvements include a higher contrast ratio and reduced off-axiscolor when used in a display system. Other improvements include areduced variation in the orientation of the transmission and block axes.

Both DBEF and APF are polymeric multilayer reflective polarizers thatinclude alternating polymeric layers. Other reflective polarizers may beused in the optical systems of the present description. In someembodiments, the reflective polarizer is a wire grid polarizer. This isillustrated in FIGS. 13A-13B which are schematic top and side views,respectively, of wire grid polarizer 1327 including a wire grid layer1375 disposed on a transparent substrate 1370. Such wire grid polarizerscan be thermoformed into a shape curved about two orthogonal axes (e.g.,the x- and y-axes). The wire grid layer 1375 include a plurality ofwires or metallic traces 1377 arranged in parallel rows (prior tothermoforming) extending in a block direction (y-direction) of thereflective polarizer.

In some embodiments, instead of using a wire grid polarizer thatincludes a wire grid layer on a substrate layer, a wire grid polarizeris formed on a lens surface by depositing metallic traces on the surfaceof the lens.

In some embodiments, an optical system includes a partial reflector, areflective polarizer, and a first quarter wave retarder disposed betweenthe reflective polarizer and the partial reflector. The partialreflector and the reflective polarizer may be adjacent to and spacedapart from one another. The optical system may include an image surfaceand a stop surface with the partial reflector disposed between the imagesurface and the stop surface, and the reflective polarizer disposedbetween the stop surface and the partial reflector. An image source maycomprise the image surface and the stop surface may be an exit pupil, oran image recorder may comprise the image surface and the stop surfacemay be an entrance pupil. The image source may include a display panelwhich may be transparent or semi-transparent and the image source mayfurther include a shutter. In some embodiments, the image surface may beadapted to receive light reflected from objects external to opticalsystem. The partial reflector has an average optical reflectance of atleast 30% in a desired or pre-determined plurality of wavelengths andmay also have an average optical transmittance of at least 30% in thedesired or pre-determined plurality of wavelengths. The desired orpre-determined plurality of wavelengths may include one or morecontinuous wavelength ranges. In some cases, the desired orpre-determined plurality of wavelengths may be the visible wavelengthrange (e.g., 400 nm to 700 nm). Both the average optical reflectance andthe average optical transmittance in the desired or pre-determinedplurality of wavelengths may be between 30% and 70%, or between 40% and60%, for example. The first quarter wave retarder, and any optionaladditional quarter wave retarders, may be a quarter wave retarder at atleast one wavelength in the desired or pre-determined plurality ofwavelengths. The quarter wave retarder(s) may be oriented so that thefast axis of the retarder is oriented at 45 degrees relative thetransmission or block axis of the reflective polarizer. The reflectivepolarizer is curved about orthogonal first and second axes. The opticalsystem may include a plurality of surfaces (e.g., the major surfaces ofone, two, three, or more optical lenses—see, e.g., FIGS. 1, 2, 5-9)disposed between the image surface and the stop surface and thereflective polarizer, the first quarter wave retarder and the partialreflector may be disposed on one or more surfaces in the plurality ofsurfaces. Any or all of the surfaces in the plurality of surfaces mayhave a shape described by an aspheric polynomial sag equation. Theoptical system may satisfy any one of the following conditions, anycombination of any 2, 3, 4, 5, 6 or 7 of the following conditions, orall of the following conditions:

-   -   (i) each of the reflective polarizer and the partial reflector        are convex toward the image surface along the orthogonal first        and second axes;    -   (ii) the reflective polarizer is a multilayer polymeric        reflective polarizer which comprises at least one layer that is        substantially optically biaxial at at least one first location        on the at least one layer away from an optical axis and        substantially optically uniaxial at at least one second location        away from the optical axis, and any or substantially any chief        light ray that passes through the image surface and the stop        surface is incident on each of the first optical stack and the        second optical stack with an angle of incidence less than about        30 degrees, or less than about 25 degrees, or less than 20        degrees;    -   (iii) an image source comprises the image surface, the image        source emitting an undistorted image, the partial reflector        having a first shape, and the reflective polarizer having a        different second shape such that a distortion of the emitted        undistorted image transmitted by the stop surface is less than        about 10% of a field of view at the stop surface;    -   (iv) any or substantially any chief light ray having at least        first and second wavelengths at least 150 nm apart in a visible        wavelength range and transmitted through the image surface and        the stop surface has a color separation distance at the stop        surface that is less than 1.5 percent, or less than 1.2 percent,        of a field of view at the stop surface or less than 20 arc        minutes, or less than 10 arc minutes;    -   (v) the reflective polarizer is a thermoformed multilayer        reflective polarizer rotationally symmetric about an optical        axis. The reflective polarizer may be APF, or DBEF, or may be a        wire grid polarizer, for example;    -   (vi) the optical system provides an adjustable prescription        (dioptric) correction. The prescription correction can be        provided by an adjustable distance between the reflective        polarizer and the partial reflector and/or an adjustable shape        of a lens disposed between the image and stop surfaces;    -   (vii) the reflective polarizer has at least one first location        having a radial distance r1 from an optical axis passing through        an apex of the reflective polarizer, and a displacement s1 from        a plane perpendicular to the optical axis at the apex. The ratio        s1/r1 is at least 0.1, or at least 0.2, and may be less than 0.8        or less than 0.6; and    -   (viii) an image source comprises the image surface, and a        contrast ratio at the stop surface is at least 40, or at least        50, or at least 60, or at least 80, or at least 100 over the        field of view of the optical system.

Any of the partial reflectors used in any of the optical systems of thepresent description may have an average optical reflectance of at least30% in a desired or pre-determined plurality of wavelengths, and/or mayhave an average optical transmittance of at least 30% in a desired orpre-determined plurality of wavelengths. The desired or pre-determinedplurality of wavelengths may be a desired or pre-determined wavelengthrange or may be a plurality of desired or pre-determined wavelengthranges. Any of the optical systems of the present description mayinclude one or more retarders which are quarter wave retarders at atleast one wavelength in the desired or pre-determined plurality ofwavelengths. The desired or pre-determined plurality of wavelengths may,for example, be any wavelength range in which the optical system isdesigned to operate. The pre-determined or desired plurality ofwavelengths may be a visible range, and may for example, be the range ofwavelengths from 400 nm to 700 nm. In some embodiments, the desired orpre-determined plurality of wavelengths may be an infrared range or mayinclude one or more of infrared, visible and ultraviolet wavelengths. Insome embodiments, the desired or pre-determined plurality of wavelengthsmay be a narrow wavelength band, or a plurality of narrow wavelengthbands, and the partial reflector may be a notch reflector. In someembodiments, the desired or pre-determined plurality of wavelengthsinclude at least one continuous wavelength range that has a full widthat half maximum of no more than 100 nm, or no more than 50 nm.

In any of the optical systems described herein, unless the contextclearly indicates differently, an image source may comprise the imagesurface and the stop surface may be an exit pupil, which may be adaptedto overlap an entrance pupil of a second optical system. The entrancepupil of the second optical system may be an entrance pupil of aviewer's eye, for example. In any of the optical systems describedherein, unless the context clearly indicates differently, an imagerecorder may comprises the image surface and the stop surface may be anentrance pupil.

Any of the optical systems of the present description may have asubstantially planar image surface and/or a substantially planar stopsurface, or one or both of these surfaces may be curved. The imagesurface may have a maximum lateral dimension A, and a stop surface mayhave a maximum lateral dimension B, where A/B is at least 2, or at least3, or at least 4, or at least 5. In some embodiments, A/B may be in arange of 2 to 20, or 3 to 10, for example.

Any of the optical systems of the present description may have a fieldof view of at least 80 degrees, of at least 90 degrees, or of at least100 degrees. Any of the optical systems of the present description maybe adapted such that at least one chief light ray transmitted throughthe stop surface and the image surface may pass through the stop surfaceat an incident angle of at least 40 degrees, or at least 45 degrees, orat least 50 degrees.

In some aspects of the present description a device is provide thatincludes any one or more of the optical systems of the presentdescription. The device may be or may include, for example, a displaydevice, such as a head-mounted display or a projection system, anilluminator, which may also be a projector, a beam expander, a camera,or a magnifying device. The magnifying device may be a telescope,binoculars, or a microscope, for example.

In some embodiments, the reflective polarizer is thermoformed. Opticalfilms, such as reflective polarizers, may have anisotropic mechanicalproperties which make obtaining a desired shape of the thermoformedoptical film difficult due to anisotropic contraction of the opticalfilm after removing the film from the thermoform mold. The anisotropicmechanical properties can arise in a multilayer polymeric reflectivepolarizer due to the anisotropic orientation of the polymeric moleculesin at least some layers of the reflective polarizer. Anisotropicmechanical properties in a wire grid polarizer comprising wires on asurface of a polymeric film can arise due to the anisotropy of the wireswhich may extend in one direction. According to the present description,methods have been found for providing an optical film having a desiredshape when the optical film has anisotropic mechanical properties.

FIG. 15 is a schematic flow chart illustrating a method 1580 of making adesired optical film having a desired shape including the steps of (i)(step 1582) providing a thermoform tool having an external surfacehaving a first shape different than the desired shape; (ii) (step 1584)heating an optical film resulting in a softened optical film; (iii)(step 1586) conforming the softened optical film to the external surfacehaving the first shape while stretching the softened film along at leastorthogonal first and second directions (e.g., the x- and y-directions ofFIG. 16) resulting in a conformed optical film having the first shape;and (iv) (step 1588) cooling the conformed optical film resulting in thedesired optical film having the desired shape. The cooling step mayinclude releasing the optical film from the tool. For example, in someembodiments, the optical film is removed from the tool and allowed tocool. In some embodiments, the method further includes the step ofmolding (e.g., film insert molding) an optical lens on the optical filmresulting in an optical stack.

In some embodiments, the desired optical film is any optical film havinganisotropic mechanical properties and may be any of the reflectivepolarizers described herein. In some embodiments, the desired opticalfilm is a reflective polarizer with a quarter wave coating or alaminated reflective polarizer film and quarter wave retarder film. Thedesired shape may be a shape that is rotationally symmetric about anoptical axis (e.g., parallel to the z-axis of FIG. 16) of the opticalfilm. The optical axis of the optical film may coincide with the opticalaxis of an optical stack that includes the optical film.

FIG. 16 is a schematic cross-sectional view of a thermoform tool 1681suitable for use in thermoforming optical films. Thermoform tool 1681includes a dome-like portion 1683 having an external surface 1685 anddisposed on a base 1687. The external surface 1685 may have a shape of aportion of an ellipsoid, for example. The ellipsoid may have a majordiameter and a minor diameter and a ratio of the major diameter to theminor diameter may be in a range of 1.01 to 1.1, or in a range of 1.01to 1.05, for example. It has been found that thermoforming a reflectivepolarizer film on such an ellipsoidal tool according to method 1580, forexample, can provide a rotationally symmetric reflective polarizer uponremoving the film from the tool and allowing the film to cool.

Any of the reflective polarizers of the present description, which maybe included in any of the optical systems of the present description,may be thermoformed according to the process 1580 and/or using thethermoform tool 1681. The reflective polarizer, and other optical films,may be integrated into an optical stack including an optical lens byinjection molding a suitable lens material (e.g., polycarbonate) ontothe film(s) in a film insert molding process, for example.

Any of the optical systems of the present description may be used in adevice such as a head-mounted display (e.g., a virtual reality display)or a camera (e.g., a camera disposed in a cell phone). FIG. 17 is aschematic top view of head-mounted display 1790 including a frame 1792,first and second display portions 1794 a and 1794 b, a camera 1796, andan eye-tracking unit 1798. First and second display portions 1794 a and1794 b include outer surfaces 1782 a and 1782 b, respectively, and innersurfaces 1784 a and 1784 b, respectively. Camera 1796 includes an outersurface 1786 and an inner surface 1788. Each of the first and seconddisplay portions 1794 a and 1794 b may include a display panelcomprising the image surface of any of the optical systems of thepresent description with a stop surface of the optical system being anexit pupil adapted to overlap an entrance pupil of a user. For example,first display portion 1794 a (and similarly for second display portion1794 b) may include the image surface 130 and the first and secondoptical stacks 110 and 120 of optical system 100. Image surface 130 maybe disposed adjacent outer surface 1782 a and the stop surface 135 maylie outside of first display portion 1794 a toward the viewer (in theminus z-direction from inner surface 1784 a). In some embodiments, asingle display panel spanning portions 1794 a and 1794 b may be usedinstead of separate display panels.

The camera 1796, which may optionally be omitted, may include anyoptical system of the present description with the stop surface anentrance pupil of the optical system and with an image recordercomprising the image surface. For example, camera 1796 may include thefirst and second optical stacks 110 and 120 of optical system 100. Imagesurface 130 may be a surface of an image recorder disposed adjacentinner surface 1788 and the stop surface 135 may be disposed adjacentouter surface 1786 or may lie outside of the camera away from the viewer(in the plus z-direction from outer surface 1786).

Head-mounted display 1790 may include three of the optical systems ofthe present description. In other embodiments, only one or two opticalsystems of the present description is included in a head-mounteddisplay. For example, in some embodiments a head-mounted display mayinclude a single optical system of the present description to provideimages to one eye of a user while the other eye has an unobstructed viewof the user's environment. In still other embodiments, more than threeoptical systems of the present description may be included. For example,two camera units each including an optical system of the presentdescription may be included to provide stereoscopic views or to providemultiple views (e.g., picture in picture) to the user while two displayunits are utilized as in FIG. 17.

The head-mounted display 1790 may include an eye-tracking systemcomprising eye-tracking unit 1798, which may optionally be omitted. Thesystem may monitor the diameter and position of a user's pupil utilizingan imaging sensor and processor. Light from a display panel included infirst portion 1798 may reflect from the user's pupil and reflect fromthe reflective polarizer of an optical system disposed in first portion1798 into eye-tracking unit 1798. Alternatively, eye-tracking unit 1798may include a light source (e.g., an infrared light source) which emitslight toward a reflective component in first portion 1794 a which isreflected towards the viewer's eye. This light then reflects from theeye and reflects from the reflective component in first portion 1794 aback towards eye-tracking unit 1798.

The attributes of the eye that the eye monitoring system can detect mayinclude one or more of the following: the viewing direction of the eye,diameter and changes in the diameter of the pupil, blinking of theeyelids, the eye tracking objects, and saccade movement. Eye trackingparameters may include velocity of the eye rotation and lag or phasebetween movement of an object and movement of the eye. Saccade movementmay include duration, velocity, and pattern of the movement. The systemmay quantify fatigue and cognitive processing load of the user of thesystem based on pupillary response with considerations of ambient lightconditions and may be personalized to the user based on historical data.

In some embodiments, the eye-tracking unit includes a camera (e.g., ared-green-blue (RGB) camera or an infrared (IR) camera) which may or maynot include an optical system of the present description and that cancapture an image of the eye. An IR camera can be used to determinedambient light conditions since the average IR luminance of the eye imageis indicative of the ambient light levels.

In some embodiments, the head-mounted display 1790 includes an eyetracking system adapted to detect changes in pupil size and use thatinformation to quantify user fatigue and cognitive processing load. Insome embodiments, the head-mounted display 1790 is adapted (e.g., usingan algorithm running on an embedded processor) to implement one or moreor all of the following steps:

Step 1: Capture a grayscale image of the eye.

Step 2: Filter out noise (e.g. using a Gaussian filter).

Step 3: Calculate gradient magnitude and direction for each pixel in theimage of the eye.

Step 4: Identify pixels with higher gradient magnitudes (these arelikely to be an edge of an object).

Step 5: Identify edges by, for example, connecting the pixels identifiedin the previous step according to the Helmholtz Principle of humanvisual perception.

Step 6: Compare edge line segments to the equation of an ellipse orother shape defined by a polynomial equation. The smallest ellipse-likeshape can be identified as the pupil. The area of the iris can also bedetermined and may be used to improve accuracy. Other elliptical shapesthat may be in the image, such as glint, can be eliminated.

Step 7: Calculate the pupil size (e.g., diameter or area) based on theline fitting done previously and the distance between the eye and thecamera.

Step 8: Determine and apply an adjustment factor to the calculated pupilsize to account for ambient light conditions. Ambient light conditionscan be determined using an additional sensor included in thehead-mounted system or via luminance analysis of the image captured.

Step 9: Optionally save the adjusted pupil size in a database. The pupilsize may be recorded as a function of time and may be stored as atime-series (a sequence of data points made over time).

The head-mounted display 1790 may be adapted to change the lightintensity generated by the display panels in first and second portions1794 a and 1794 b based on pupil size and/or pupil direction informationdetermined using eye-tracking unit 1798. The eye-tracking system may beconfigured to detect where in the virtual image that the user is lookingand the optical system may be adapted to adjust the virtual imagedistance to match the depth of the object as presented stereoscopicallyby adjusting the positions of one or more lenses in the optical systemas described elsewhere herein.

In some embodiments, head-mounted display 1790 is configured so thatprescription lenses may be attached adjacent inner surfaces 1784 aand/or 1784 b.

In some aspects of the present description, a device is provided thatincludes an optical system of the present description. An example ofsuch a device is a head-mounted display such as head-mounted display1790 that include one or more of the optical systems of the presentdescription. FIG. 24A is a schematic top view of a device 2490 thatincludes optical system 2400. Optical system 2400 includes a reflectivepolarizer 2427, a partial reflector 2417, and a first quarter waveretarder 2425 disposed between the reflective polarizer 2427 and thefirst quarter wave retarder 2425. The reflective polarizer 2427, thepartial reflector 2417, and the first quarter wave retarder 2425 maycorrespond to any of the reflective polarizers, the partial reflectorsor the quarter wave retarders described elsewhere herein. For example,in some embodiments the reflective polarizer 2427 is a polymericmultilayer reflective polarizer (e.g., APF) and in some embodiments thereflective polarizer 2427 is a wire grid polarizer. The reflectivepolarizer 2427 may be curved about orthogonal first and second axes andmay be thermoformed into the desired shape. The partial reflector 2417may be curved about orthogonal first and second axes or mayalternatively be flat or curved about only one axis. Similarly, thefirst quarter wave retarder 2425 may be curved about orthogonal firstand second axes or may alternatively be flat or curved about only oneaxis. The reflective polarizer 2427, the partial reflector 2417, and thefirst quarter wave retarder 2425 may be disposed on surfaces of one ormore lenses as described elsewhere herein.

Device 2490 can be, for example, a display device, a beam expander, acamera, or a magnifying device such as a telescope, a microscope,binoculars or the like. In the case of binoculars or head-mounteddisplays, more than one optical system 2400 may be included. Forexample, two of optical systems 2400 (one for each eye) may be included;an example of a device including two optical systems is illustrated inFIG. 24C. In display applications, the optical system 2400 may beoriented with the partial reflector 2417 facing an image forming device(e.g., a display panel) of the display. In camera applications, theoptical system 2400 may be oriented with the reflective polarizer 2427facing an entrance pupil of the camera and with the partial reflector2417 facing the object or environment to be viewed. A stop surface ofthe optical system 2400 may be an aperture adapted to receive lightreflected from objects external to the optical system 2400, and an imagesurface of the optical system 2400 may be a surface of an imagerecorder. In telescope, microscope, and binoculars applications, theoptical system 2400 may be used in an objective portion device or may beused in an eyepiece of the device with the reflective polarizer facingthe viewer in either case. An image surface of the optical system 2400may be adapted to receive light reflected from objects external to theoptical system 2400, and a stop surface of the optical system 2400 maybe an exit pupil adapted to overlap a pupil of the viewer.

FIG. 24B is a schematic top view of a display device 2490 b whichincludes the optical system 2400 of FIG. 24A. Display device 2490includes a transparent or semi-transparent display panel 2431 and ashutter 2493. As described elsewhere herein, the transparent orsemi-transparent display panel 2431 may be an OLED or an LCD panel, forexample, and the shutter 2493 may be a PDLC shutter, for example. Thedisplay panel 2431 is illustrated as convex toward the reflectivepolarizer 2417. In other embodiments, the display panel 2431 may beconcave toward the reflective polarizer 2417. In still otherembodiments, the display panel 2431 may be flat or substantially flat(and may have a substantially planar image surface). The display panel2431 (and its image surface) may be curved about two orthogonal axes ormay be curved about only one axis. The shutter 2493 may have the sameshape or a different shape than the display panel 2431. The shutter 2493may be curved about two orthogonal axes, or curved about only one axes,or may be substantially flat (substantially planar). The shutter 2493may be utilized to allow ambient light to enter the optical system 2400or to block ambient light from entering the optical system 2400. Displaydevice 2490 b may include an optional additional polarizer 2468 disposedbetween the optical system 2400 and the display panel 2431. Optionaladditional polarizer 2468 may be a linear polarizer and may be areflective polarizer or an absorbing polarizer. In some embodiments,optional additional polarizer 2468 is not included or may be included asa component of the display panel 2431, for example. The optionaladditional polarizer 2468 may be substantially flat as illustrated ormay be curved about one axis or about two orthogonal axes.

FIG. 24C is a schematic top view of a device 2490 c that includes firstoptical system 2400-1 in an eyepiece portion 2497-1 and includes secondoptical system 2400-2 in an eyepiece portion 2497-2. Device 2490 c maybe binoculars or a microscope, for example. First optical system 2400-1includes a reflective polarizer 2427-1, a partial reflector 2417-1, anda quarter wave retarder 2425-1 disposed between the reflective polarizer2427-1 and the quarter wave retarder 2425-1. Second optical system2400-2 includes a reflective polarizer 2427-2, a partial reflector2417-2, and a quarter wave retarder 2425-2 disposed between thereflective polarizer 2427-2 and the quarter wave retarder 2425-2. Thereflective polarizers 2427-1 and 2427-2, the partial reflectors 2417-1and 2417-2, and the quarter wave retarders 2425-1 and 2425-1 maycorrespond to any of the reflective polarizers, the partial reflectorsor the quarter wave retarders described elsewhere herein. The reflectivepolarizers 2427-1 and 2427-2 may be curved about orthogonal first andsecond axes and may be thermoformed into the desired shape. The partialreflectors 2417-1 and 2417-2 may optionally also be curved aboutorthogonal first and second axes or may be flat as illustrated or curvedabout only one axis. Similarly, the quarter wave retarders 2425-1 and2425-2 may be curved about orthogonal first and second axes or may beflat as illustrated or curved about only one axis. The reflectivepolarizers 2427-1 and 2427-2, the partial reflectors 2417-1 and 2417-2,and the quarter wave retarders 2425-1 and 2425-2 may be disposed onsurfaces of one or more lenses as described elsewhere herein.

Device 2490 c includes an objective portion 2499-1 and an objectiveportion 2499-2. The objective portions 2499-1 and 2499-2 are adapted toface an object being viewed and the eyepiece portions are adapted toface a viewer's eyes. An image surface of optical system 2400-1 (andsimilarly for optical system 2400-2) may be between the partialreflector 2417-1 and the objective portion 2499-1, may be within theobjective portion 2499-1 or may be between the eyepiece portion 2497-1and the objective portion 2499-1. A stop surface of the optical system2400-1 (and similarly for optical system 2400-2) may be an exit pupiladapted to overlap a pupil of a user.

The objective portion 2499-1 may contain one or more optical lenses2491-1 and the objective portions 2499-2 may contain one or more opticallenses 2491-2. In alternate embodiments, the eyepiece portion 2497-1 andthe objective portion 2499-1 are provided without the eyepiece portion2497-2 and the objective portion 2499-2 for use as a telescope ormicroscope.

FIG. 25 is a schematic side view of a device 2590 a including device2590, which may include any of the optical systems described herein, andilluminator 2502 a, which includes polarizing beam splitting system 2504a. Device 2590 a may be described as an illuminator, for example, andmay be a compact projection system, for example. Polarizing beamsplitting system 2504 a includes polarizing beam splitter 2500 a andfirst and second reflective components 2532 a and 2534 a. Illuminator2502 a further includes a light source 2550 a. Polarizing beam splitter2500 a, which may correspond to polarizing beam splitter 100, includesfirst and second prisms 2510 a and 2520 a, and reflective polarizer 2530a. First prism 2510 a includes input face 2512 a, output face 2514 a andfirst hypotenuse 2516 a. Input face 2512 a has an input active area 2513a and output face 2514 a has an output active area 2515 a. Device 2590has largest acceptance area 2543 a. Second prism 2520 a has an imagerface 2524 a and a second hypotenuse 2526 a. A reflective polarizer 2530a is disposed between first and second hypotenuses 2516 a and 2526 a.The light source 2550 a produces a light beam having an envelope 2552 aand a central light ray 2556 a which defines a folded optical axis 2557a having first, second, third and fourth segments, 2557 a-1 through 2557a-4. The first reflective component 2532 a is disposed adjacent thepolarizing beam splitter 2500 a opposite light source 2550 a and thesecond reflective component 2534 a is disposed adjacent the polarizingbeam splitter 2500 a opposite device 2590.

In some embodiments, the first prism 2510 a has a first volume, thesecond prism 2520 a has a second volume, and the first volume is nogreater than about half (or no greater than about 60 percent, or nogreater than about 40 percent) of the second volume.

Device 2590 may be a beam expander and may correspond to device 2490.Device 2590 may include a reflective polarizer, a partial reflector anda first quarter wave retarder disposed between the reflective polarizerand the partial reflector. When used as a beam expander, device 2590 maybe adapted to receive an input light beam incident on the partialreflector and transmit an expanded output light beam. For example, theinput light beam may be converging or collimated and the output lightbeam may be diverging, or the input light beam may have a firstdivergence angle and the output light beam may have a greater seconddivergence angle. The device 2590 may be oriented such that the partialreflector faces the illuminator 2502 a. An additional polarizer (e.g.,an additional reflective polarizer or an absorbing polarizer) may bedisposed between device 2590 and output face 2514 a, or may be includedin device 2590 proximate the partial reflector opposite the reflectivepolarizer. Illuminator 2502 a may provide a compact illumination systemand device 2590 may be used as a beam expander to provide a wider fieldof view. Other illuminators that can be used with device 2590 aredescribed in U.S. Provisional App. No. 62/186,944 entitled“Illuminator”, filed on Jun. 30, 2015, and hereby incorporated herein byreference to the extent that it does not contradict the presentdescription. Device 2590 may be a beam expander including a partialreflector and a reflective polarizer adjacent to and spaced apart fromone another, and the beam expander may be adapted to receive converginglight incident on the partial reflector and transmit diverging lightthrough the reflective polarizer.

The second reflective component 2534 a has a largest active area 2536 a.The second reflective component 2534 a may be an image forming deviceand the largest active area 2536 a may be a largest image area of theimage forming device. Light is emitted (by being reflected, for example)from second reflective component 2534 a in envelope 2554 a. One or bothof the first and second reflective components 2532 a and 2534 a may havea specular reflectance of greater than 70 percent, or greater than 80percent, or greater than 90 percent. The first and/or second reflectivecomponents 2532 a and 2534 a may be flat or may be curved in one or moreaxes.

In some embodiments, second reflective component 2534 a is adapted tomodulate light incident thereon. For example, second reflectivecomponent 2534 a may be an image forming device that reflects lighthaving a spatially modulated polarization state. Second reflectivecomponent 2534 a may be pixelated and may produce a patterned light.Light reflected from second reflective component 2534 a in envelope 2554a may be converging patterned light. Suitable image forming devices thatcan be utilized as second reflective component 2534 a include LiquidCrystal on Silicon (LCoS) devices. The LCoS device may be flat or may becurved in one or more axes.

The various components in FIG. 25 are shown spaced apart for clarity ofillustration. However, it should be understood that the variouscomponents could be in direct contact or attached through an opticallyclear adhesive, for example. In some embodiments, reflective polarizer2530 a is attached to one or both of first and second prisms 2510 a and2520 a using optically clear adhesive layers. In some embodiments,device 2590 is attached to output face 2514 a with an optically clearadhesive. In some embodiments, light source 2550 a may be immediatelyadjacent input face 2512 a or may be attached to input face 2512 athrough an optically clear adhesive layer. In some embodiments, firstand/or second reflective components 2532 a and 2534 a may be attached tosecond prism 2520 a with optically clear adhesives. The reflectivepolarizer 2530 a may be any of the reflective polarizers describedelsewhere herein. In some embodiments, the reflective polarizer 2530 ais a polymeric multilayer reflective polarizer, a wire grid polarizer, aMacNeille reflective polarizer, or a cholesteric reflective polarizer.

Folded optical axis 2557 a includes first segment 2557 a-1 extending ina first direction (positive x-direction) from the light source 2550 a tothe first reflective component 2532 a, second segment 2557 a-2 extendingin a second direction (negative x-direction) opposite the firstdirection, third segment 2557 a-3 extending in a third direction(negative y-direction), and fourth segment 2557 a-4 extending in afourth direction (positive y-direction) opposite the third direction.First and second segments 2557 a-1 and 2557 a-2 are overlapping thoughthey are shown with a small separation in FIG. 25 for ease ofillustration. Similarly, third and fourth segments 2557 a-3 and 2557 a-4are overlapping though they are shown with a small separation in FIG. 25for ease of illustration. The first and second directions aresubstantially orthogonal to the third and fourth directions. The firstreflective component 2532 a is substantially perpendicular to the firstsegment 2557 a-1 and the second reflective component 2534 a issubstantially perpendicular to the third segment 2557 a-3.

Light source 2550 a produces a light beam having envelope 2552 a andthis defines the input active area 2513 a as the area of input face 2512a that is illumined with light from the light source 2550 a that is usedby the illuminator 2502 a. Light source 2550 a may either substantiallynot produce light outside of the envelope 2552 a or any light that isproduced outside this envelope is at an angle that it escapes from theilluminator without entering device 2590.

At least a portion of the light from light source 2550 a is, insequence, transmitted through the first prism 2510 a, transmittedthrough the reflective polarizer 2530 a, transmitted through the secondprism 2520 a, reflected from the first reflective component 2532 a,transmitted back through the second prism 2520 a, reflected from thereflective polarizer 2530 a, transmitted through the second prism 2520 aand is incident on second reflective component 2534 a, reflected fromsecond reflective component 2534 a, transmitted through second prism2520 a and reflective polarizer 2530 a and first prism 2510 a, andfinally exits the illuminator through device 2590. This is illustratedin FIG. 25 for central light ray 2556 a. In some embodiments, firstreflective component 2532 a includes a polarization rotator, which maybe a quarter wave retarder. Light from the light source 2550 a that hasa polarization along the pass axis of reflective polarizer 2530 a willbe transmitter through the reflective polarizer 2530 a and then reflectfrom first reflective component 2532 a back towards the reflectivepolarizer 2530 a. In embodiments in which first reflective component2532 a includes a quarter wave retarder, such light passes twice throughthe quarter wave retarder when it reflects back toward the reflectivepolarizer 2530 a. This light then has a polarization substantiallyorthogonal to the pass axis of the reflective polarizer 2530 a and soreflects from the reflective polarizer 2530 a toward second reflectivecomponent 2534 a which may emit (e.g., reflect) spatially modulatedlight back toward reflective polarizer 2530 a. The spatially modulatedlight may have a polarization that is spatially modulated. The portionof the spatially modulated light having a polarization along the passaxis of reflective polarizer 2530 a will pass through the reflectivepolarizer 2530 a as an imaged light, exit first prism 2510 a throughoutput active area 2515 a and exit the illuminator through the device2590.

The illuminator 2502 a allows an image to be projected by directing alight beam (in envelope 2552 a) through a folded light path illuminator2502 a onto an imaging forming device (second reflective component 2534a), and reflecting a converging patterned light (in envelope 2554 a)from the image forming device. The step of directing a light beamthrough the folded light path illuminator 2502 a includes directinglight to the first reflective component 2532 a through the polarizingbeam splitter 2500 a, reflecting at least some of the light back towardsthe polarizing beam splitter 2500 a, and reflecting at least some of thelight from the polarizing beam splitter 2500 a towards the image formingdevice. At least a portion of the converging patterned light istransmitted through the polarizing beam splitter 2500 a and throughdevice 2590.

Light from light source 2550 a illuminates a maximum area of secondreflective component 2534 a after the light is reflected from the firstreflective component 2532 a and the reflective polarizer 2530 a. Thismaximum area may be equal to the largest active area 2536 a.Alternatively, the largest active area 2536 a may be a largest area ofsecond reflective component 2534 a that is reflective. For example,second reflective component 2534 a may be an image forming device thathas a largest image area. Any light incident on the image forming deviceoutside the largest image area may not be reflected towards device 2590.In this case, the largest active area 2536 a would be the largest imagearea of the image forming device. The largest active area 2536 a definesthe output active area 2515 a on output face 2514 a and largestacceptance area 2543 a of device 2590 since light is reflected from thelargest active area 2536 a towards device 2590 in envelope 2554 a whichilluminates the output face 2514 a substantially only in the outputactive area 2515 a and illuminates the device 2590 substantially only inthe largest acceptance area 2543 a. Illuminator 2502 a is configuredsuch that light in envelope 2554 a that is reflected from the secondreflective component 2534 a and that passes through the device 2590 isconvergent between the second reflective component 2534 a and the device2590. This results in a largest active area 2536 a that is smaller thanthe output active area 2515 a which is smaller than the largest activearea 2536 a.

In some embodiments, the input active area 2513 a and/or the outputactive area 2515 a are less than about 60 percent, or less than about 50percent (i.e., less than about half), or less than about 40 percent, orless than about 35 percent of the largest active area 2536 a, which maybe a largest image area. In some embodiments, the largest surface areaof input face 2512 a (the total area of input face 2512 a) is less thanabout half the largest image area. In some embodiments, the largestsurface area of the output face 2514 a (the total area of output face2514 a) is less than about half the largest image area.

Light source 2550 a, or any of the light sources of the presentdescription, may include one or more substantially monochromatic lightemitting elements. For example, light source 2550 a may include red,green and blue light emitting diodes (LEDs). Other colors, such as cyanand yellow may also be included. Alternatively, or in addition, broadspectrum (e.g., white or substantially white) light sources may beutilized. In some embodiments, the light source 2550 a includes a blueemitter and a phosphor. In some embodiments, the light source 2550 aincludes an integrator that may be utilized to combine light fromdiscrete light sources (e.g., the integrator may combine light from red,green and blue LEDs). The light source 2550 a may include a polarizingelement such that light having substantially a single polarization stateis directed into first prism 2510 a towards reflective polarizer 2530 a.In some embodiments, light source 2550 a may be or may include one ormore of an LED, an organic light emitting diode (OLED), a laser, a laserdiode, an incandescent lighting element, and an arc lamp. Light source2550 a may also include a lens, such as a condenser lens, in addition tolighting emitting element(s) such as LED(s). In some embodiments, thefirst or second prisms may have one or more curved faces to provide adesired optical power.

The optical systems of the present description may include one or morelenses having a non-uniform edge profile, which may be designed toconform to a face when used as a component of a head-mounted display.The lens(es) may have an edge profile to conform to an average face, tocategories of face shapes, or may be designed for individual faces.

FIG. 27A is a perspective view of an optical system 2700 of ahead-mounted display positioned on a head 10 with a vertical profile ofthe head 10 centered on the right eye 12. The lenses of the opticalsystem 2700 providing a gap or relief 18 from the eyebrow and a gap orrelief 16 from the cheek. Optical system 2700 includes display panel2731 and may correspond to any of the optical systems of the presentdescription where a display panel can comprise an image surface of theoptical system. FIG. 27B is a top view of the optical system 2700 withthe lenses of the optical system 2700 providing a relief 26 from thetemple and a relief 28 from the bridge of the nose.

FIG. 27C is another top view of the optical system 2700. A display panel2731 has pixels 34 a, 34 b, and 34 c emitting light that is focused bythe lenses of the optical system into the eye of the head. The chief ray38 of the light from pixel 34 a passes to the eye with an incidenceangle of 46 degrees. The greater extent of the relief of the lensassembly 36 from the temple allows the chief ray 40 from pixel 34 c tobe passed to the eye with a higher incidence angle of 60 degrees.

The reliefs of the lens assembly may be created in the molding of thelenses making up the lens assembly. Alternatively, the lenses may becustom ground for individuals using appropriate measurements of theface. Relief provided for the lens can restrict the area of the displayvisible to the user. In some embodiments, the relief data is provided toa computer controlling display panel 2731 and the computer may limit thedisplay area to the regions visible to the user in order to reduce powerconsumption and/or in order to reduce visible artifacts from ghostimages, for example.

An advantage of providing a consistent amount of relief of the lens fromthe face is that ambient light can be effectively blocked with the imagewhile still providing adequate air circulation near the eye. Utilizingextended surfaces of the lens(es) of the optical systems can improveboth the field of view and comfort to the user.

EXAMPLES Example 1

An optical system similar to optical system 200 was modeled. A secondquarter wave retarder was disposed on second major surface 216. Each ofthe surfaces corresponding to surfaces 224, 226, 214 and 216 were takento be aspheric surfaces described by Equation 1 with each of thepolynomial coefficients D, E, F, G, H, I . . . equal to zero. The conicconstant k was 0.042435 and the surface radius, r=1/c, was −36.82391 mm.Table 1 lists the parameters describing each of these surfaces.

TABLE 1 Radius Thickness Diameter Surf. Type (mm) (mm) Material (mm)Conic OBJ STANDARD Infinity Infinity 0 0 STO STANDARD Infinity 23.820415 0 2 EVENASPH −36.82391 2.19729 POLYCARB 46.22652 0.04243522 3EVENASPH −36.82391 10.34174 48.50417 0.04243522 4 EVENASPH −36.82391−10.34174 MIRROR 58.17894 0.04243522 5 EVENASPH −36.82391 10.34174MIRROR 44.64956 0.04243522 6 EVENASPH −36.82391 2.19729 E48R 600.04243522 7 EVENASPH −36.82391 2 62 0.04243522 IMA STANDARD Infinity54.72404 0

The surface numbers in this table count the times that a ray startingfrom stop surface 235 (Surf. 1) and ending at the image surface 230(Surf. 8 or IMA) is incident on a surface. Surf. 2 corresponds to firstsurface 224, Surf. 3 and Surf. 5 correspond to second surface 226, Surf.4 and Surf 6 correspond to first surface 214, and Surf 7 corresponds tosurface 216. The diameter refers to the clear aperture of the surface,EVENASPH refers to even asphere (only even powers of r appear in theexpansion in Equation 1), the radius is the inverse of the parameter cin Equation 1, conic is the parameter k in Equation 1, and IMA refers tothe image surface 230.

The first optical lens 212 was modeled as Zenon E48R having a refractiveindex of 1.53 and the second optical lens 222 was modeled aspolycarbonate having a refractive index of 1.585. The focal length was32.26271 mm, the field of view was 90 degrees, the image height was27.14 mm (the diameter of the image surface 230 was 54.28 mm), the F#was 2.13, the eye relief (distance from stop surface to first lenssurface) was 23.8 mm, and the eye box (diameter of the stop surface 235)was 15 mm.

Each chief light ray that was emitted by the image surface and that wastransmitted through the stop surface was incident on each of the firstoptical stack and the second optical stack at an angle of incidence lessthan about 20 degrees each time the chief light ray was incident on thefirst or second optical stack.

The optical system had a field of view of 90 degrees at the stopsurface. Chief light rays having wavelengths of 486 nm and 656 nm whichwere transmitted through the image surface and the stop surface had amaximum color separation distance at the stop surface of 3.4 arc minuteswhich was about 0.12 percent of the field of view at the stop surface.

Example 2

An optical system similar to optical system 200 was modeled. A secondquarter wave retarder was disposed on second major surface 216. Each ofthe surfaces corresponding to surfaces 224, 226, 214 and 216 were takento be aspheric surfaces described by Equation 1. Tables 2 and 3 list theparameters describing each of these surfaces. The nomenclature in thetables is similar to that in Example 1. The units for the asphericpolynomial coefficients in Table 3 are mm to 1 minus the power of thepolynomial.

TABLE 2 Radius Thickness Diameter Surf. Type (mm) (mm) Material (mm)Conic OBJ STANDARD Infinity −250 500 0 STO STANDARD Infinity 15 6.848 02 EVENASPH −23.17192 2.5 POLYCARB 25 0 3 EVENASPH −18.85196 4.69107326.56958 0.5582269 4 EVENASPH −19.44056 −4.691073 MIRROR 30.63103−9.582783 5 EVENASPH −18.85196 4.691073 MIRROR 24.31869 0.5582269 6EVENASPH −19.44056 2 E48R 31 −9.582783 7 EVENASPH −19.44056 0.621 31−9.582783 8 STANDARD Infinity 0.281 PMMA 28.60935 0 9 STANDARD Infinity0.01 28.66299 0 10 STANDARD Infinity 0.7 N-BK7 28.66585 0 11 STANDARDInfinity 0 28.79723 0 IMA STANDARD Infinity 28.79723 0

TABLE 3 Polynomial Coefficient order parameter Surf. 3, 5 Surf. 4, 6, 7r{circumflex over ( )}2 D 0.000000E+00 0.000000E+00 r{circumflex over( )}4 E 1.245489E−05 −1.462422E−04 r{circumflex over ( )}6 F1.393604E−07 9.569876E−07 r{circumflex over ( )}8 G −1.860081E−09−6.019644E−09  r{circumflex over ( )}10 H 2.407929E−11 2.373262E−11 r{circumflex over ( )}12 I −1.266371E−13 −5.331213E−14  r{circumflexover ( )}14 J 2.853295E−16 4.901801E−17

The surface numbers in these tables count the times that a ray startingfrom stop surface 235 (Surf. 1) and ending at the image surface 230(Surf. 12 or IMA) is incident on a surface. Surf. 2 corresponds to firstsurface 224, Surf. 3 and Surf. 5 correspond to second surface 226, Surf4 and Surf. 6 correspond to first surface 214, and Surf. 7 correspondsto surface 216. Surfs. 8-11 refer to surface layers disposed on theimage surface 230.

The first optical lens 212 was modeled as Zenon E48R having a refractiveindex of 1.53 and the second optical lens 222 was modeled aspolycarbonate having a refractive index of 1.585. The focal length was17.560 mm, the field of view was 90 degrees, the image height was 14.36mm (the diameter of the image surface 230 was 28.72 mm), the F# was2.55, the eye relief was 15 mm, and the eye box (diameter of stopsurface 235) was 10.0 mm.

Each chief light ray that was emitted by the image surface and that wastransmitted through the stop surface was incident on each of the firstoptical stack and the second optical stack at an angle of incidence lessthan about 20 degrees each time the chief light ray was incident on thefirst or second optical stack.

The optical system had a field of view of 90 degrees at the stopsurface. Chief light rays having wavelengths of 486 nm and 656 nm whichwere transmitted through the image surface and the stop surface had amaximum color separation distance at the stop surface of 10.8 arcminutes which was about 0.38 percent of the field of view at the stopsurface.

Example 3

An optical system similar to optical system 600 was modeled. Each of thesurfaces corresponding to surfaces 614 and 616 were taken to be asphericsurfaces described by Equation 1. Tables 4 and 5 list the parametersdescribing each of these surfaces. The nomenclature in the table aresimilar to that in Examples 1 and 2.

TABLE 4 Radius Thickness Surf. Type (mm) (mm) Material Diameter ConicOBJ STANDARD Infinity Infinity 0 0 STO STANDARD Infinity 19.43519 15 0 2EVENASPH −32.97361 6.734839 POLYCARB 42.67275 −0.6680006 3 EVENASPH−32.97361 −6.734839 MIRROR 49.63501 −0.6680006 4 EVENASPH −32.973616.734839 MIRROR 42.06153 −0.6680006 5 EVENASPH −32.97361 21.7945546.89222 −0.6680006 IMA STANDARD Infinity 66.72897 0

TABLE 5 Polynomial Coefficient order parameter Surf. 2, 3, 4, 5r{circumflex over ( )}2 D 0 r{circumflex over ( )}4 E −2.231952E−06r{circumflex over ( )}6 F −1.907497E−09 r{circumflex over ( )}8 G1.062720E−12  r{circumflex over ( )}10 H −5.475949E−15  r{circumflexover ( )}12 I 6.686581E−18  r{circumflex over ( )}14 J −4.780909E−21

The surface numbers in these tables count the times that a ray startingfrom stop surface 635 (Surf. 1) and ending at the image surface 630(Surf. 6 or IMA) is incident on a surface. Surf. 2 and Surf. 4correspond to first surface 614, and Surf 3 and Surf 5 correspond tosecond surface 616,

The focal length was 35.0 mm, the field of view was 90 degrees, theimage height was 33.3 mm (the diameter of the image surface 630 was 66.6mm), the F# was 2.3, the eye relief was 19.4 mm, and the eye box(diameter of stop surface 635) was 15 mm.

Each chief light ray that was emitted by the image surface and that wastransmitted through the stop surface was incident on each of the firstoptical stack and the second optical stack at an angle of incidence lessthan about 20 degrees each time the chief light ray was incident on thefirst or second optical stack.

The optical system had a field of view of 90 degrees at the stopsurface. Chief light rays having wavelengths of 486 nm and 656 nm whichwere transmitted through the image surface and the stop surface had amaximum color separation distance at the stop surface of 29.5 arcminutes which was about 0.9 percent of the field of view at the stopsurface.

Example 4

An optical system similar to optical system 800 was modeled. Areflective polarizer was disposed on second major surface 866 of thirdoptical lens 862 and a first quarter wave retarder was disposed on thereflective polarizer. A partial reflector was disposed on first majorsurface 824 of second optical lens 822 and a second quarter waveretarder was disposed on second major surface 826 of second optical lens822. Each of the surfaces corresponding to surfaces 864, 866, 824, 826,814, and 816 were taken to be aspheric surfaces described by Equation 1.Tables 6 and 7 list the parameters describing each of these surfaces.The nomenclature in the tables is similar to that in the previousExamples.

TABLE 6 Radius Thickness Diameter Surf. Type (mm) (mm) Material (mm)Conic OBJ STANDARD Infinity Infinity 0 0 STO STANDARD Infinity 11.014759 0 2 EVENASPH −16.25782 2 POLYCARB 21.26634 0 3 EVENASPH −17.445412.513635 23.93589 0.7369043 4 EVENASPH −16.75009 −2.513635 MIRROR25.75788 −0.1016067 5 EVENASPH −17.44541 2.513635 MIRROR 23.357470.7369043 6 EVENASPH −16.75009 5 E48R 24.5425 −0.1016067 7 EVENASPH−12.77019 1 26.71183 −0.491206 8 EVENASPH −157.2536 6 E48R 30.82226−11.8657 9 EVENASPH −18.4783 6.867862 31.77972 −0.4304748 IMA STANDARDInfinity 32.24099 0

TABLE 7 Polynomial Coefficient order parameter Surf. 3, 5 Surf. 9r{circumflex over ( )}2 D 0.000000E+00 0.000000E+00 r{circumflex over( )}4 E 3.286842E−05 1.398664E−04 r{circumflex over ( )}6 F 1.861485E−07−5.794668E−07 r{circumflex over ( )}8 G −1.944055E−09 1.220044E−09 r{circumflex over ( )}10 H 1.540250E−11 −9.383593E−13  r{circumflexover ( )}12 I 0.000000E+00 0.000000E+00  r{circumflex over ( )}14 J0.000000E+00 0.000000E+00

The surface numbers in these tables count the times that a ray startingfrom stop surface 835 (Surf. 1) and ending at the image surface 830(Surf. 10 or IMA) is incident on a surface. Surf. 2 corresponds to firstsurface 864, Surf. 3 and Surf. 5 correspond to second surface 866, Surf.4 and Surf. 6 correspond to first surface 824, Surf. 7 corresponds tosurface 266, Surf. 8 corresponds to surface 814, and Surf. 9 correspondsto surface 816.

The focal length was 19.180 mm, the field of view was 82 degrees, theimage height was 15.89 mm (the diameter of the image surface 830 was31.87 mm), the F# was 2.12, the eye relief was 11 mm, and the eye box(diameter of stop surface 835) was 9 mm.

Each chief light ray that was emitted by the image surface and that wastransmitted through the stop surface was incident on each of the firstoptical stack and the second optical stack at an angle of incidence lessthan about 20 degrees each time the chief light ray was incident on thefirst or second optical stack.

The optical system had a field of view of 80 degrees at the stopsurface. Chief light rays having wavelengths of 486 nm and 656 nm whichwere transmitted through the image surface and the stop surface had amaximum color separation distance at the stop surface of 14.9 arcminutes which was about 0.52 percent of the field of view at the stopsurface.

Example 5

An optical system similar to optical system 200 was modeled. A secondquarter wave retarder was disposed on second major surface 216. Each ofthe surfaces corresponding to surfaces 224, 226, 214 and 216 were takento be aspheric surfaces described by Equation 1 with each of thepolynomial coefficients D, E, F, G, H, I . . . equal to zero. Table 8lists the parameters describing each of these surfaces with thenomenclature similar to that in previous Examples.

TABLE 8 Radius Thickness Diameter Surf. Type (mm) (mm) Material (mm)Conic OBJ STANDARD Infinity Infinity 0 0 STO STANDARD Infinity 25 15 0 2EVENASPH −40.49115 4.85538 E48R 49.67147 0.7502449 3 EVENASPH −40.491158.498641 54.28738 0.7502449 4 EVENASPH −40.24456 −8.498641 MIRROR 630.2694101 5 EVENASPH −40.49115 8.498641 MIRROR 50.62275 0.7502449 6EVENASPH −40.24456 5.013904 POLYCARB 63 0.2694101 7 EVENASPH −31.1818514.48671 67 −3.575525 IMA STANDARD Infinity 102.1176 0

The surface numbers in this table count the times that a ray startingfrom stop surface 235 (Surf. 1) and ending at the image surface 230(Surf. 8 or IMA) is incident on a surface. Surf. 2 corresponds to firstsurface 224, Surf. 3 and Surf. 5 correspond to second surface 226, Surf.4 and Surf 6 correspond to first surface 214, and Surf 7 corresponds tosurface 216. The diameter refers to the clear aperture of the surface,EVENASPH refers to even asphere (only even powers of r appear in theexpansion in Equation 1), the radius is the inverse of the parameter cin Equation 1, conic is the parameter k in Equation 1, and IMA refers tothe image surface 230.

The first optical lens 212 was modeled as Zenon E48R having a refractiveindex of 1.53 and the second optical lens 222 was modeled aspolycarbonate having a refractive index of 1.585. The focal length was42.7 mm, the field of view was 100 degrees, the image height was 50.94mm (the diameter of the image surface 230 was 101.88 mm), the F# was3.25, the eye relief was 25 mm, and the eye box (diameter of the stopsurface 235) was 15 mm.

Each chief light ray that was emitted by the image surface and that wastransmitted through the stop surface was incident on each of the firstoptical stack and the second optical stack at an angle of incidence lessthan about 20 degrees each time the chief light ray was incident on thefirst or second optical stack.

The optical system had a field of view of 100 degrees at the stopsurface. Chief light rays having wavelengths of 486 nm and 656 nm whichwere transmitted through the image surface and the stop surface had amaximum color separation distance at the stop surface of 11.9 arcminutes which was about 0.29 percent of the field of view at the stopsurface.

An undistorted image produced at image surface 230 was simulated and thedistortion of the image at the stop surface 235 was determined to beless than 1 percent.

Examples 6-8

DBEF (Example 6), APF (Example 7) and APF with a quarter wave retardercoating (Example 8) were thermoformed to give the films a geometrymatching to the geometry of an outer surface of a lens. The films weretrimmed to fit in an injection molding tool lens cavity and placed on asurface of the lens cavity. The trimmed films had a diameter of 63 mmand a radius of curvature of 87 mm. An injection mold polycarbonateresin was used to form the lens on the film. The films were formed onthe side of the lens that would face the stop surface when used in anoptical system of the present description. In Example 7, the film wasformed on the lens so that when used in an optical system of the presentdescription, the APF would face the stop surface and the quarter waveretarder faced away from the stop surface.

The thermoforming of the films were done in a MAAC sheet feedthermoforming system using vacuum to pull the heated film onto anexternal surface of a thermoform tool similar to thermoform tool 1681.The external surface was approximately ellipsoidal shaped with the majoraxis about 1.02 times the minor axis so that the resulting thermoformedfilm would be rotationally symmetric after cooling and relaxing. Thethermoforming process parameters were: Sheet Oven Temperature=320°F.−380° F. (160° C.−193° C.); Forming Time=18 seconds; and Sheet FormingTemperature=330° F.−365° F. (156° C.−185° C.).

Images of the thermoformed DBEF (Example 6) and APF (Example 7)reflective polarizer samples were taken using a non-polarizednear-Lambertian light source to emit light through the samples to acamera that included an analyzing polarizer aligned with the block axisof the analyzing polarizer at varying angles from the block axis of thereflective polarizer. At zero degrees both films were substantiallytransparent and at higher angles, the DBEF showed optical artifacts thatwere not present in the APF sample. For example, at an angle of 70degrees, the APF sample was substantially uniformly dark while the DBEFsample showed colored rings. The film insert injection molding processwas done in a reciprocating screw horizontal clamp injection moldingsystem built by Krauss-Maffei (Germany). The injection molding toolingused was for a 6 base lens part and a Bayer MAKROLON 3107-550115polycarbonate resin (available from Bayer MaterialScience LLC,Pittsburgh, Pa.) was used to form the lens. The injection moldingprocess parameters were: Mold Temperature=180° F. (82° C.); MeltTemperature=560° F. (293° C.); Fill Time=1.56 seconds; Hold Time=5.5seconds; Hold Pressure=11,000 psi (75.8 MPa); Cool Time=15 seconds.

Examples 9-11

Reflective polarizers were thermoformed as generally described inExamples 6-8 into a convex rotationally symmetric shape having adiameter of 50.8 mm and a radius of curvature of 38.6 mm. The reflectivepolarizers were DBEF (Example 9), APF (Example 10) and a wire gridpolarizer (Example 11). The polarizance orientation was measured foreach sample using an Axometrics AXOSCAN polarimeter (available fromAxometrics, Inc., Huntsville, Ala.). For each sample, an area of thesample centered on the apex of the film and having a 20 mm diametercircular aperture was identified and the maximum variation of atransmission axis of the sample (maximum angular deviation of thetransmission axis from a fixed direction minus minimum angular deviationof the transmission axis from the fixed direction) in the aperture wasdetermined. For DBEF, the maximum variation was 1.707 degrees, for APFthe maximum variation was 0.751 degrees, and for the wire gridpolarizer, the maximum variation was 0.931 degrees. The boundary of thearea had a sag of 1.32 mm at a radial distance of 10 mm from arotational symmetry axis of the samples.

The following is a list of exemplary embodiments.

Embodiment 1 is an optical system, comprising:

-   an image surface;-   a stop surface;-   a first optical stack disposed between the image surface and the    stop surface and convex toward the image surface along orthogonal    first and second axes, the first optical stack comprising:    -   a first optical lens; and    -   a partial reflector having an average optical reflectance of at        least 30% in a desired plurality of wavelengths; and-   a second optical stack disposed between the first optical stack and    the stop surface and convex toward the image surface along the first    and second axes, the second optical stack comprising:    -   a second optical lens;    -   a multilayer reflective polarizer substantially transmitting        light having a first polarization state and substantially        reflecting light having an orthogonal second polarization state;        and    -   a first quarter wave retarder disposed between the reflective        polarizer and the first optical stack.        Embodiment 2 is the optical system of embodiment 1, wherein an        image source comprises the image surface and the stop surface is        an exit pupil.        Embodiment 3 is the optical system of embodiment 2, wherein the        image source comprises a display panel.        Embodiment 4 is the optical system of embodiment 3, wherein the        display panel is transparent or semi-transparent.        Embodiment 5 is the optical system of any of embodiments 2 to 4,        wherein the image source comprises a shutter.        Embodiment 6 is the optical system of embodiment 1, wherein the        image source comprises an aperture adapted to receive light        reflected from objects external to the optical system.        Embodiment 7 is the optical system of embodiment 1, wherein an        image recorder comprises the image surface and the stop surface        is an entrance pupil.        Embodiment 8 is the optical system of any of embodiments 1 to 7,        wherein the optical system is centered on a folded optical axis        defined by an optical path of a central light ray transmitted        through the image surface.        Embodiment 9 is the optical system of any of embodiments 1 to 8,        wherein the stop surface is adapted to overlap an entrance pupil        of a second optical system.        Embodiment 10 is the optical system of embodiment 9, wherein the        second optical system is adapted to record images received at        the entrance pupil.        Embodiment 11 is the optical system of embodiment 1, wherein the        stop surface is adapted to overlap an entrance pupil of a        viewer's eye.        Embodiment 12 is the optical system of embodiment 1, wherein an        image source comprises the image surface, the image source        emitting unpolarized light.        Embodiment 13 is the optical system of any of embodiments 1 to        12, wherein the first optical stack further comprises a second        quarter wave retarder disposed between the partial reflector and        the image surface.        Embodiment 14 is the optical system of embodiment 1, wherein an        image source comprises the image surface, the image source        emitting polarized light.        Embodiment 15 is the optical system of embodiment 14, wherein        the polarized light is linearly polarized.        Embodiment 16 is the optical system of embodiment 14, wherein        the polarized light is circularly polarized.        Embodiment 17 is the optical system of embodiment 14, wherein        the polarized light is elliptically polarized.        Embodiment 18 is the optical system of any of embodiments 1 to        17, wherein the partial reflector is a second reflective        polarizer.        Embodiment 19 is the optical system of any of embodiments 1 to        18, wherein the partial reflector has an average optical        transmittance of at least 30% in the desired plurality of        wavelengths.        Embodiment 20 is the optical system of any of embodiments 1 to        19, wherein the desired plurality of wavelengths comprise at        least one continuous wavelength range.        Embodiment 21 is the optical system of any of embodiments 1 to        20, wherein the desired plurality of wavelengths comprises a        visible range of wavelengths.        Embodiment 22 is the optical system of embodiment 21, wherein        the visible range is from 400 nm to 700 nm.        Embodiment 23 is the optical system of any of embodiments 1 to        20, wherein the desired plurality of wavelengths comprises an        infrared range of wavelengths.        Embodiment 24 is the optical system of any of embodiments 1 to        20, wherein the desired plurality of wavelengths comprises one        or more of infrared, visible and ultraviolet wavelengths.        Embodiment 25 is the optical system of any of embodiments 1 to        21, wherein the partial reflector is a notch reflector.        Embodiment 26 is the optical system of embodiment 25, wherein        the desired plurality of wavelengths comprises one or more        continuous wavelength ranges, and wherein at least one of the        continuous wavelength ranges has a full width at half maximum of        no more than 100 nm.        Embodiment 27 is the optical system of embodiment 26, wherein        the full width at half maximum is no more than 50 nm.        Embodiment 28 is the optical system of any of embodiments 1 to        27, wherein the multilayer reflective polarizer has at least one        first location having a radial distance, r1, from an optical        axis passing through an apex of the multilayer reflective        polarizer, and a displacement, s1, from a plane perpendicular to        the optical axis at the apex, s1/r1 being at least 0.1.        Embodiment 29 is the optical system of embodiment 28, wherein        s1/r1 is at least 0.2.        Embodiment 30 is the optical system of embodiment 28, wherein        s1/r1 is in a range of 0.2 to 0.8.        Embodiment 31 is the optical system of embodiment 28, wherein        s1/r1 is in a range of 0.3 to 0.6.        Embodiment 32 is the optical system of any of embodiments 28 to        31, wherein the multilayer reflective polarizer has a second        location having a radial distance, r2, from the optical axis and        a displacement, s2, from the plane, s2/r2 being at least 0.3.        Embodiment 33 is the optical system of any of embodiments 1 to        27, wherein the multilayer reflective polarizer has at least one        first location having a radial distance, r1, from an optical        axis passing through an apex of the multilayer reflective        polarizer and a displacement, s1, from a plane perpendicular to        the optical axis at the apex, s1/r1 being at least 0.2, and        wherein for an area of the reflective polarizer defined by s1        and r1, a maximum variation of a transmission axis of the        reflective polarizer is less than about 2 degrees.        Embodiment 34 is the optical system of embodiment 33, wherein        the maximum variation of the transmission axis of the reflective        polarizer is less than about 1.5 degrees.        Embodiment 35 is the optical system of any of embodiments 1 to        34, wherein a maximum variation of a transmission axis of the        reflective polarizer in a reflection aperture of the reflective        polarizer is less than about 1.5 degrees.        Embodiment 36 is the optical system of any of embodiments 1 to        34, wherein a maximum variation of a transmission axis of the        reflective polarizer in a reflection aperture of the reflective        polarizer is less than about 1 degree.        Embodiment 37 is the optical system of any of embodiments 1 to        36, wherein the image surface has a maximum lateral dimension A,        the stop surface has a maximum lateral dimension B, and A/B is        at least 3.        Embodiment 38 is the optical system of any of embodiments 1 to        37, wherein the first optical lens has a first major surface        facing the second optical lens and an opposing second major        surface facing the image surface, and the second optical lens        has a first major surface facing the stop surface and an        opposing second major surface facing the first optical lens.        Embodiment 39 is the optical system of embodiment 38, wherein        the partial reflector is disposed on the first or second major        surface of the first lens.        Embodiment 40 is the optical system of embodiment 38, wherein        the partial reflector is disposed on the first major surface of        the first lens and a second quarter wave retarder is disposed on        the second major surface of the first lens.        Embodiment 41 is the optical system of embodiment 38, wherein        the partial reflector is disposed on the second major surface of        the first lens and a second quarter wave retarder is disposed on        the partial reflector opposite the second major surface of the        first lens.        Embodiment 42 is the optical system of embodiment 38, wherein a        second quarter wave retarder is disposed on the first major        surface of the first optical lens and the partial reflector is        disposed on the second quarter wave retarder opposite the first        major surface of the first optical lens.        Embodiment 43 is the optical system of embodiment 38, wherein        the first quarter wave retarder is disposed on the second major        surface of the second optical lens and the multilayer reflective        polarizer is disposed on the first major surface of the second        optical lens.        Embodiment 44 is the optical system of embodiment 38, wherein        the multilayer reflective polarizer is disposed on the second        major surface of the second optical lens and the first quarter        wave retarder is disposed on the multilayer reflective polarizer        opposite the second major surface of the second optical lens.        Embodiment 45 is the optical system of any of embodiments 1 to        44, wherein the multilayer reflective polarizer comprises at        least one layer that is substantially optically biaxial at at        least one first location on the at least one layer away from an        optical axis of the second optical stack and substantially        optically uniaxial at at least one second location away from the        optical axis.        Embodiment 46 is the optical system of any of embodiments 1 to        45, wherein the multilayer reflective polarizer is a        thermoformed multilayer reflective polarizer substantially        rotationally symmetric about an optical axis of the second        optical stack.        Embodiment 47 is the optical system of any of embodiments 1 to        46, wherein the multilayer reflective polarizer is a        thermoformed multilayer reflective polarizer rotationally        symmetric about an optical axis of the second optical stack.        Embodiment 48 is the optical system of any of embodiments 1 to        47, wherein substantially any chief light ray that passes        through the image surface and the stop surface is incident on        each of the first optical stack and the second optical stack        with an angle of incidence less than about 25 degrees.        Embodiment 49 is the optical system of any of embodiments 1 to        48, wherein the first and second optical stacks have a        substantially same shape.        Embodiment 50 is the optical system of any of embodiments 1 to        48, wherein the first and second optical stacks have different        shapes.        Embodiment 51 is the optical system of any of embodiments 1 to        50, wherein each of the first and second lenses are plano        lenses.        Embodiment 52 is the optical system of any of embodiments 1 to        48, wherein the first and second optical lenses have a        substantially same shape.        Embodiment 53 is the optical system of any of embodiments 1 to        48, wherein the first and second optical lenses have different        shapes.        Embodiment 54 is the optical system of any of embodiments 1 to        53, wherein the image surface is substantially planar.        Embodiment 55 is the optical system of any of embodiments 1 to        53, wherein the image surface is curved.        Embodiment 56 is the optical system of embodiment 1, wherein an        image source comprises the image surface, the image source        emitting an undistorted image, the partial reflector having a        first shape, and the reflective polarizer having a different        second shape such that a distortion of the emitted undistorted        image transmitted by the stop surface is less than about 10% of        a field of view at the stop surface.        Embodiment 57 is the optical system of embodiment 56, wherein        the distortion of the emitted undistorted image transmitted by        the stop surface is less than 5% of a field of view at the stop        surface.        Embodiment 58 is the optical system of embodiment 56, wherein        the distortion of the emitted undistorted image transmitted by        the stop surface is less than 3% of a field of view at the stop        surface.        Embodiment 59 is the optical system of any of embodiments 1 to        58, wherein substantially any chief light ray having at least        first and second wavelengths at least 150 nm apart in a visible        wavelength range and transmitted through the image surface and        the stop surface has a color separation distance at the stop        surface of less than 1.5 percent of a field of view at the stop        surface.        Embodiment 60 is the optical system of embodiment 59, wherein        the color separation distance at the stop surface is less than        1.2 percent of the field of view at the stop surface.        Embodiment 61 is the optical system of any of embodiments 1 to        60, wherein substantially any chief light ray having at least        first and second wavelengths at least 150 nm apart in a visible        wavelength range and transmitted through the image surface and        the stop surface has a color separation distance at the stop        surface of less than 20 arc minutes.        Embodiment 62 is the optical system of embodiment 61, wherein        the color separation distance at the stop surface is less than        10 arc minutes.        Embodiment 63 is the optical system of any of embodiments 1 to        62, wherein the partial reflector has a first shape, the        multilayer reflective polarizer has a second shape, and one or        both of the first and second shapes is described by an aspheric        polynomial sag equation.        Embodiment 64 is the optical system of any of embodiments 1 to        63, wherein the multilayer reflective polarizer comprises        alternating polymeric layers.        Embodiment 65 is the optical system of any of embodiments 1 to        64, wherein the multilayer reflective polarizer is APF.        Embodiment 66 is the optical system of any of embodiments 1 to        64, wherein the multilayer reflective polarizer is thermoformed        APF.        Embodiment 67 is the optical system of any of embodiments 1 to        64, wherein the multilayer reflective polarizer comprises a wire        grid polarizer.        Embodiment 68 is the optical system of any of embodiments 1 to        67, wherein the multilayer reflective polarizer is rotationally        symmetric.        Embodiment 69 is the optical system of any of embodiments 1 to        68, wherein at least one of the first and second optical stacks        have an adjustable position relative to the stop and image        surfaces.        Embodiment 70 is the optical system of any of embodiments 1 to        69, wherein at least one of the first and second optical stacks        have an adjustable shape.        Embodiment 71 is an optical system, comprising:-   an image surface;-   a stop surface;-   a first optical stack disposed between the image surface and the    stop surface and comprising:    -   a first optical lens;    -   a partial reflector having an average optical reflectance of at        least 30% in a desired plurality of wavelengths; and-   a second optical stack disposed between the first optical stack and    the stop surface and comprising:    -   a second optical lens;    -   a multilayer reflective polarizer comprising at least one layer        substantially optically biaxial at at least one first location        on the at least one layer away from an optical axis of the        second optical stack and substantially optically uniaxial at at        least one second location away from the optical axis; and    -   a first quarter wave retarder disposed between the reflective        polarizer and the first optical stack,-   wherein substantially any chief light ray that passes through the    image surface and the stop surface is incident on each of the first    optical stack and the second optical stack with an angle of    incidence less than about 30 degrees.    Embodiment 72 is the optical system of embodiment 71, wherein an    image source comprises the image surface and the stop surface is an    exit pupil.    Embodiment 73 is the optical system of embodiment 72 wherein the    image source comprises a display panel.    Embodiment 74 is the optical system of embodiment 73, wherein the    display panel is transparent or semi-transparent.    Embodiment 75 is the optical system of any of embodiments 72 to 74,    wherein the image source comprises a shutter.    Embodiment 76 is the optical system of embodiment 71, wherein the    image source comprises an aperture adapted to receive light    reflected from objects external to the optical system.    Embodiment 77 is the optical system of embodiment 71, wherein an    image recorder comprises the image surface and the stop surface is    an entrance pupil.    Embodiment 78 is the optical system of any of embodiments 71 to 77,    wherein the optical system is centered on a folded optical axis    defined by an optical path of a central light ray transmitted    through the image surface.    Embodiment 79 is the optical system of any of embodiments 71 to 78,    wherein the stop surface is adapted to overlap an entrance pupil of    a second optical system.    Embodiment 80 is the optical system of embodiment 79, wherein the    second optical system is adapted to record images received at the    entrance pupil.    Embodiment 81 is the optical system of embodiment 71, wherein the    stop surface is adapted to overlap an entrance pupil of a viewer's    eye.    Embodiment 82 is the optical system of embodiment 71, wherein an    image source comprises the image surface, the image source emitting    unpolarized light.    Embodiment 83 is the optical system of any of embodiments 71 to 82,    wherein the first optical stack further comprises a second quarter    wave retarder disposed between the partial reflector and the image    surface.    Embodiment 84 is the optical system of embodiment 71, wherein an    image source comprises the image surface, the image source emitting    polarized light.    Embodiment 85 is the optical system of embodiment 84, wherein the    polarized light is linearly polarized.    Embodiment 86 is the optical system of embodiment 84, wherein the    polarized light is circularly polarized.    Embodiment 87 is the optical system of embodiment 84, wherein the    polarized light is elliptically polarized.    Embodiment 88 is the optical system of any of embodiments 71 to 87,    wherein the partial reflector is a second reflective polarizer.    Embodiment 89 is the optical system of any of embodiments 71 to 88,    wherein the partial reflector has an average optical transmittance    of at least 30% in the desired plurality of wavelengths.    Embodiment 90 is the optical system of any of embodiments 71 to 89,    wherein the desired plurality of wavelengths comprise at least one    continuous wavelength range.    Embodiment 91 is the optical system of any of embodiments 71 to 90,    wherein the desired plurality of wavelengths comprises a visible    range of wavelengths.    Embodiment 92 is the optical system of embodiment 91, wherein the    visible range is from 400 nm to 700 nm.    Embodiment 93 is the optical system of any of embodiments 71 to 92,    wherein the desired plurality of wavelengths comprises an infrared    range of wavelengths.    Embodiment 94 is the optical system of any of embodiments 71 to 93,    wherein the desired plurality of wavelengths comprises one or more    of infrared, visible and ultraviolet wavelengths.    Embodiment 95 is the optical system of any of embodiments 71 to 91,    wherein the partial reflector is a notch reflector.    Embodiment 96 is the optical system of embodiment 95, wherein the    desired plurality of wavelengths comprises one or more continuous    wavelength ranges, and wherein at least one of the continuous    wavelength ranges has a full width at half maximum of no more than    100 nm.    Embodiment 97 is the optical system of embodiment 96, wherein the    full width at half maximum is no more than 50 nm.    Embodiment 98 is the optical system of any of embodiments 71 to 97,    wherein the multilayer reflective polarizer has at least one first    location having a radial distance, r1, from an optical axis passing    through an apex of the multilayer reflective polarizer, and a    displacement, s1, from a plane perpendicular to the optical axis at    the apex, s1/r1 being at least 0.1.    Embodiment 99 is the optical system of embodiment 98, wherein s1/r1    is at least 0.2.    Embodiment 100 is the optical system of embodiment 98, wherein s1/r1    is in a range of 0.2 to 0.8.    Embodiment 101 is the optical system of embodiment 98, wherein s1/r1    is in a range of 0.3 to 0.6.    Embodiment 102 is the optical system of any of embodiments 98 to    101, wherein the multilayer reflective polarizer has a second    location having a radial distance, r2, from the optical axis and a    displacement, s2, from the plane, s2/r2 being at least 0.3.    Embodiment 103 is the optical system of any of embodiments 71 to 97,    wherein the multilayer reflective polarizer has at least one first    location on the film having a radial distance, r1, from an optical    axis passing through an apex of the multilayer reflective polarizer    and a displacement, s1, from a plane perpendicular to the optical    axis at the apex, s1/r1 being at least 0.2, and wherein for an area    of the reflective polarizer defined by s1 and r1, a maximum    variation of a transmission axis of the reflective polarizer is less    than about 2 degrees.    Embodiment 104 is the optical system of embodiment 103, wherein the    maximum variation of the transmission axis of the reflective    polarizer is less than about 1.5 degrees.    Embodiment 105 is the optical system of any of embodiments 71 to    104, wherein a maximum variation of a transmission axis of the    reflective polarizer in a reflection aperture of the reflective    polarizer is less than about 1.5 degrees.    Embodiment 106 is the optical system of any of embodiments 71 to    104, wherein a maximum variation of a transmission axis of the    reflective polarizer in a reflection aperture of the reflective    polarizer is less than about 1 degree.    Embodiment 107 is the optical system of any of embodiments 71 to    106, wherein the first optical lens has a first major surface facing    the second optical lens and an opposing second major surface facing    the image surface, and the second optical lens has a first major    surface facing the stop surface and an opposing second major surface    facing the first optical lens.    Embodiment 108 is the optical system of embodiment 107, wherein the    partial reflector is disposed on the first or second major surface    of the first lens.    Embodiment 109 is the optical system of embodiment 108, wherein the    partial reflector is disposed on the first major surface of the    first lens and a second quarter wave retarder is disposed on the    second major surface of the first lens.    Embodiment 110 is the optical system of embodiment 108, wherein the    partial reflector is disposed on the second major surface of the    first lens and a second quarter wave retarder is disposed on the    partial reflector opposite the second major surface of the first    lens.    Embodiment 111 is the optical system of embodiment 107, wherein a    second quarter wave retarder is disposed on the first major surface    of the first optical lens and the partial reflector is disposed on    the second quarter wave retarder opposite the first major surface of    the first optical lens.    Embodiment 112 is the optical system of embodiment 107, wherein the    first quarter wave retarder is disposed on the second major surface    of the second optical lens and the multilayer reflective polarizer    is disposed on the first major surface of the second optical lens.    Embodiment 113 is the optical system of embodiment 107, wherein the    multilayer reflective polarizer is disposed on the second major    surface of the second optical lens and the first quarter wave    retarder is disposed on the multilayer reflective polarizer opposite    the second major surface of the second optical lens.    Embodiment 114 is the optical system of any of embodiments 71 to    113, wherein the image surface has a maximum lateral dimension A,    the stop surface has a maximum lateral dimension B, and A/B is at    least 3.    Embodiment 115 is the optical system of any of embodiments 71 to    114, wherein the multilayer reflective polarizer is a thermoformed    multilayer reflective polarizer substantially rotationally symmetric    about an optical axis of the second optical stack.    Embodiment 116 is the optical system of any of embodiments 71 to    115, wherein the multilayer reflective polarizer is a thermoformed    multilayer reflective polarizer rotationally symmetric about an    optical axis of the second optical stack.    Embodiment 117 is the optical system of any of embodiments 71 to    116, wherein one or both of the first and second optical stacks is    convex toward the image surface along orthogonal first and second    axes.    Embodiment 118 is the optical system of embodiment 117, wherein both    the first and second optical stacks are convex toward the image    surface along the first and second axes.    Embodiment 119 is the optical system of any of embodiments 71 to    118, wherein the multilayer reflective polarizer is convex toward    the image surface along orthogonal first and second axes.    Embodiment 120 is the optical system of any of embodiments 71 to    119, wherein the first and second optical stacks have a    substantially same shape.    Embodiment 121 is the optical system of any of embodiments 71 to    119, wherein the first and second optical stacks have different    shapes.    Embodiment 122 is the optical system of any of embodiments 71 to    121, wherein each of the first and second lenses are plano lenses.    Embodiment 123 is the optical system of any of embodiments 71 to    119, wherein the first and second optical lenses have a    substantially same shape.    Embodiment 124 is the optical system of any of embodiments 71 to    119, wherein the first and second optical lenses have different    shapes.    Embodiment 125 is the optical system of any of embodiments 71 to    124, wherein the image surface is substantially planar.    Embodiment 126 is the optical system of any of embodiments 71 to    124, wherein the image surface is curved.    Embodiment 127 is the optical system of any of embodiments 71 to    126, wherein substantially any chief light ray that passes through    the image surface and the stop surface is incident on each of the    first optical stack and the second optical stack with an angle of    incidence less than about 25 degrees.    Embodiment 128 is the optical system of embodiment 71, wherein an    image source comprises the image surface, the image source emitting    an undistorted image, the partial reflector having a first shape,    and the reflective polarizer having a different second shape such    that a distortion of the emitted undistorted image transmitted by    the stop surface is less than about 10% of a field of view at the    stop surface.    Embodiment 129 is the optical system of embodiment 128, wherein the    distortion of the emitted undistorted image transmitted by the stop    surface is less than 5% of a field of view at the stop surface.    Embodiment 130 is the optical system of embodiment 128, wherein the    distortion of the emitted undistorted image transmitted by the stop    surface is less than 3% of a field of view at the stop surface.    Embodiment 131 is the optical system of any of embodiments 71 to    130, wherein substantially any chief light ray having at least first    and second wavelengths at least 150 nm apart in a visible wavelength    range and transmitted through the image surface and the stop surface    has a color separation distance at the stop surface of less than 1.5    percent of a field of view at the stop surface.    Embodiment 132 is the optical system of embodiment 131, wherein the    color separation distance at the stop surface is less than 1.2    percent of the field of view at the stop surface.    Embodiment 133 is the optical system of any of embodiments 71 to    132, wherein substantially any chief light ray having at least first    and second wavelengths at least 150 nm apart in a visible wavelength    range and transmitted through the image surface and the stop surface    has a color separation distance at the stop surface of less than 20    arc minutes.    Embodiment 134 is the optical system of embodiment 133, wherein the    color separation distance at the stop surface is less than 10 arc    minutes.    Embodiment 135 is the optical system of any of embodiments 71 to    134, wherein the partial reflector has a first shape, the multilayer    reflective polarizer has a second shape, and one or both of the    first and second shapes is described by an aspheric polynomial sag    equation.    Embodiment 136 is the optical system of any of embodiments 71 to    135, wherein the multilayer reflective polarizer comprises    alternating polymeric layers.    Embodiment 137 is the optical system of any of embodiments 71 to    136, wherein the multilayer reflective polarizer is thermoformed    APF.    Embodiment 138 is the optical system of any of embodiments 71 to    136, wherein the multilayer reflective polarizer comprises a wire    grid polarizer.    Embodiment 139 is the optical system of any of embodiments 71 to    138, wherein the multilayer reflective polarizer is rotationally    symmetric.    Embodiment 140 is the optical system of any of embodiments 71 to    139, wherein at least one of the first and second optical stacks    have a user-adjustable position relative to the stop and image    surfaces.    Embodiment 141 is the optical system of any of embodiments 71 to    140, wherein at least one of the first and second optical stacks    have a user-adjustable shape.    Embodiment 142 is an optical system, comprising:-   an image source emitting an undistorted image;-   an exit pupil;-   a partial reflector having a first shape convex toward the image    source along orthogonal first and second axes and having an average    optical reflectance of at least 30% in a pre-determined plurality of    wavelengths; and-   a reflective polarizer having a different second shape convex toward    the image source along the first and second axes, such that a    distortion of the emitted undistorted image transmitted by the exit    pupil is less than about 10%.    Embodiment 143 is the optical system of embodiment 142, wherein the    distortion of the emitted undistorted image transmitted by the exit    pupil is less than about 5%.    Embodiment 144 is the optical system of embodiment 142, wherein the    distortion of the emitted undistorted image transmitted by the exit    pupil is less than about 3%.    Embodiment 145 is the optical system of any of embodiments 142 to    144, wherein an integral optical stack disposed between the image    source and the exit pupil comprises a first optical lens, a first    quarter wave retarder, the partial reflector and the reflective    polarizer.    Embodiment 146 is the optical system of embodiment 145, wherein the    first quarter wave retarder is disposed on a first major surface of    the first optical lens facing the image source, and the partial    reflector is disposed on the quarter wave retarder opposite the    first optical lens.    Embodiment 147 is the optical system of embodiment 145, wherein the    partial reflector is disposed on a first major surface of the first    optical lens facing the image source.    Embodiment 148 is the optical system of embodiment 147, wherein the    first quarter wave retarder is disposed on a second major surface of    the first optical lens opposite the first major surface.    Embodiment 149 is the optical system of embodiment 147, wherein the    reflective polarizer is disposed on the first quarter wave retarder    opposite the first optical lens.    Embodiment 150 is the optical system of any of embodiments 145 to    149, wherein the integral optical stack further comprises a second    quarter wave retarder.    Embodiment 151 is the optical system of embodiment 150, wherein the    second quarter wave retarder is disposed on a major surface of the    partial reflector facing the image source.    Embodiment 152 is the optical system of any of embodiments 142 to    151, wherein substantially any chief light ray having at least first    and second wavelengths at least 150 nm apart in the pre-determined    plurality of wavelengths and emitted by the image source and    transmitted by the exit pupil has a color separation distance at the    exit pupil of less than 1.5 percent of a field of view at the exit    pupil.    Embodiment 153 is the optical system of any of embodiments 142 to    152, wherein substantially any chief light ray having at least first    and second wavelengths at least 150 nm apart in the pre-determined    plurality of wavelengths and emitted by the image source and    transmitted by the exit pupil has a color separation distance at the    exit pupil of less than 20 arc minutes.    Embodiment 154 is an optical system, comprising:-   an image source;-   an exit pupil;-   a first optical stack disposed between the image source and the exit    pupil and comprising:    -   a first optical lens;    -   a partial reflector having an average optical reflectance of at        least 30% in a pre-determined plurality of wavelengths; and-   a second optical stack disposed between the first optical stack and    the exit pupil and comprising:    -   a second optical lens;    -   a multilayer reflective polarizer; and    -   a first quarter wave retarder disposed between the reflective        polarizer and the first optical stack,-   wherein substantially any chief light ray having at least first and    second wavelengths at least 150 nm apart in the pre-determined    plurality of wavelengths and emitted by the image source and    transmitted by the exit pupil has a color separation distance at the    exit pupil of less than 1.5 percent of a field of view at the exit    pupil, and wherein the multilayer reflective polarizer is convex    about two orthogonal axes.    Embodiment 155 is the optical system of embodiment 154, wherein the    color separation distance at the exit pupil is less than 1.2 percent    of the field of view at the exit pupil.    Embodiment 156 is the optical system of embodiment 154 or 155,    wherein the color separation distance at the exit pupil is less than    20 arc minutes.    Embodiment 157 is the optical system of any of embodiments 154 to    155, wherein the color separation distance at the exit pupil is less    than 10 arc minutes.    Embodiment 158 is an optical system, comprising:-   an image source;-   an exit pupil;-   a first optical stack disposed between the image source and the exit    pupil and comprising:    -   a first optical lens;    -   a partial reflector having an average optical reflectance of at        least 30% in a pre-determined plurality of wavelengths; and-   a second optical stack disposed between the first optical stack and    the exit pupil and comprising:    -   a second optical lens;    -   a multilayer reflective polarizer; and    -   a first quarter wave retarder disposed between the reflective        polarizer and the first optical stack,-   wherein substantially any chief light ray having at least first and    second wavelengths at least 150 nm apart in the pre-determined    plurality of wavelengths and emitted by the image source and    transmitted by the exit pupil has a color separation distance at the    exit pupil of less than 20 arc minutes, and wherein the multilayer    reflective polarizer is convex about two orthogonal axes.    Embodiment 159 is the optical system of embodiment 158, wherein the    color separation distance at the exit pupil is less than 10 arc    minutes.    Embodiment 160 is the optical system of embodiment 158 or 159,    wherein the color separation distance at the exit pupil is less than    1.5 percent of a field of view at the exit pupil.    Embodiment 161 is the optical system of any of embodiments 158 to    160, wherein the color separation distance at the exit pupil is less    than 1.2 percent of a field of view at the exit pupil.    Embodiment 162 is the optical system of any of embodiments 154 to    160, wherein at least one of the first and second optical stacks    have an adjustable position relative to the stop and image surfaces.    Embodiment 163 is the optical system of any of embodiments 154 to    162, wherein at least one of the first and second optical stacks    have an adjustable shape.    Embodiment 164 is the optical system of any of embodiments 154 to    163, wherein the first optical stack in convex toward the image    source along orthogonal first and second axes.    Embodiment 165 is the optical system of any of embodiments 154 to    164, wherein the second optical stack in convex toward the image    source along orthogonal first and second axes.    Embodiment 166 is the optical system of any of embodiments 142 to    165, wherein the image source has a maximum lateral dimension A, the    exit pupil has a maximum lateral dimension B, and A/B is at least 3.    Embodiment 167 is the optical system of any of embodiments 142 to    166, wherein at least one chief light ray from the image source    passes through the exit pupil at an incident angle of at least 40    degrees.    Embodiment 168 is the optical system of any of embodiments 142 to    167, wherein the optical system is centered on a folded optical axis    defined by an optical path of a central light emitted by the image    source.    Embodiment 169 is the optical system of any of embodiments 142 to    168, wherein the exit pupil is adapted to overlap an entrance pupil    of a second optical system.    Embodiment 170 is the optical system of embodiment 169, wherein the    second optical system is adapted to record images received at the    entrance pupil.    Embodiment 171 is the optical system of any of embodiments 142 to    169, wherein the exit pupil is adapted to overlap an entrance pupil    of a viewer's eye.    Embodiment 172 is the optical system any of embodiments 142 to 171,    wherein the image source emits unpolarized light.    Embodiment 173 is the optical system of any of embodiments 142 to    171, wherein the image source emits polarized light.    Embodiment 174 is the optical system of embodiment 173, wherein the    polarized light is linearly polarized.    Embodiment 175 is the optical system of embodiment 173, wherein the    polarized light is circularly polarized.    Embodiment 176 is the optical system of embodiment 173, wherein the    polarized light is elliptically polarized.    Embodiment 177 is the optical system of any of embodiments 142 to    176, wherein the partial reflector is a second reflective polarizer.    Embodiment 178 is the optical system of any of embodiments 142 to    177, wherein the partial reflector has an average optical    transmittance of at least 30% in the pre-determined plurality of    wavelengths.    Embodiment 179 is the optical system of any of embodiments 142 to    178, wherein the pre-determined plurality of wavelengths comprise    one or more pre-determined wavelength ranges.    Embodiment 180 is the optical system of any of embodiments 142 to    179, wherein the wherein the pre-determined plurality of wavelengths    comprise a visible range.    Embodiment 181 is the optical system of embodiment 180, wherein the    visible range is from 400 nm to 700 nm.    Embodiment 182 is the optical system of any of embodiments 142 to    179, wherein the pre-determined plurality of wavelengths comprise an    infrared range.    Embodiment 183 is the optical system of any of embodiments 142 to    179, wherein the pre-determined plurality of wavelengths comprises    one or more of infrared, visible and ultraviolet wavelengths.    Embodiment 184 is the optical system of any of embodiments 142 to    180, wherein the partial reflector is a notch reflector.    Embodiment 185 is the optical system of embodiment 184, wherein the    pre-determined plurality of wavelengths comprises at least one    wavelength range having a full width at half maximum of no more than    100 nm.    Embodiment 186 is the optical system of embodiment 184, wherein the    pre-determined plurality of wavelengths comprises at least one    wavelength range having a full width at half maximum of no more than    50 nm.    Embodiment 187 is the optical system any of embodiments 142 to 186,    wherein the reflective polarizer has at least one first location    having a radial distance, r1, from an optical axis passing through    an apex of the multilayer reflective polarizer, and a displacement,    s1, from a plane perpendicular to the optical axis at the apex,    s1/r1 being at least 0.1.    Embodiment 188 is the optical system of embodiment 187, wherein    s1/r1 is at least 0.2.    Embodiment 189 is the optical system of embodiment 187, wherein    s1/r1 is in a range of 0.2 to 0.8.    Embodiment 190 is the optical system of embodiment 187, wherein    s1/r1 is in a range of 0.3 to 0.6.    Embodiment 191 is the optical system of any of embodiments 187 to    190, wherein the multilayer reflective polarizer has a second    location having a radial distance, r2, from the optical axis and a    displacement, s2, from the plane, s2/r2 being at least 0.3.    Embodiment 192 is the optical system of any of embodiments 142 to    186, wherein the multilayer reflective polarizer has at least one    first location having a radial distance, r1, from an optical axis    passing through an apex of the reflective polarizer and a    displacement, s1, from a plane perpendicular to the optical axis at    the apex, s1/r1 being at least 0.2, and wherein for an area of the    reflective polarizer defined by s1 and r1, a maximum variation of a    transmission axis of the reflective polarizer is less than about 2    degrees.    Embodiment 193 is the optical system of embodiment 192, wherein the    maximum variation of the transmission axis of the reflective    polarizer is less than about 1.5 degrees.    Embodiment 194 is the optical system of any of embodiments 142 to    193, wherein a maximum variation of a transmission axis of the    reflective polarizer in a reflection aperture of the reflective    polarizer is less than about 1.5 degrees.    Embodiment 195 is the optical system of any of embodiments 142 to    193, wherein a maximum variation of a transmission axis of the    reflective polarizer in a reflection aperture of the reflective    polarizer is less than about 1 degree.    Embodiment 196 is the optical system of any of embodiments 142 to    195, wherein the reflective polarizer comprises at least one layer    that is substantially optically biaxial at at least one first    location on the at least one layer away from an optical axis of the    second optical stack and substantially optically uniaxial at at    least one second location away from the optical axis.    Embodiment 197 is the optical system of any of embodiments 142 to    196, wherein the reflective polarizer is a thermoformed multilayer    reflective polarizer substantially rotationally symmetric about an    optical axis of the reflective polarizer.    Embodiment 198 is the optical system of any of embodiments 142 to    197, wherein the reflective polarizer is a thermoformed multilayer    reflective polarizer rotationally symmetric about an optical axis of    the reflective polarizer.    Embodiment 199 is the optical system of any of embodiments 142 to    198, wherein substantially any chief light ray that is emitted by    the image source and that is transmitted through the exit pupil is    incident on each of the reflective polarizer and the partial    reflector with an angle of incidence less than about 25 degrees.    Embodiment 200 is the optical system of any of embodiments 142 to    202, wherein the partial reflector has a first shape, the reflective    polarizer has a second shape, and one or both of the first and    second shapes is described by an aspheric polynomial sag equation.    Embodiment 201 is the optical system of any of embodiments 142 to    200, wherein the reflective polarizer comprises alternating    polymeric layers.    Embodiment 202 is the optical system of any of embodiments 142 to    201, wherein the reflective polarizer is thermoformed APF.    Embodiment 203 is the optical system of any of embodiments 142 to    201, wherein the reflective polarizer comprises a wire grid    polarizer.    Embodiment 204 is the optical system of any of embodiments 142 to    203, wherein the reflective polarizer is rotationally symmetric.    Embodiment 205 is the optical system of any of embodiments 142 to    204, wherein the image source comprises a display panel.    Embodiment 206 is the optical system of embodiment 205, wherein the    display panel is transparent or semi-transparent.    Embodiment 207 is the optical system of embodiment 204 or 205,    wherein the image source comprises a shutter.    Embodiment 208 is an optical system, comprising:-   an image surface having a maximum lateral dimension A;-   a stop surface having a maximum lateral dimension B, A/B being at    least 3;-   an integral optical stack disposed between the image surface and the    stop surface and comprising:    -   a first optical lens;    -   a partial reflector having an average optical reflectance of at        least 30% in a pre-determined plurality of wavelengths;    -   a multilayer reflective polarizer substantially transmitting        light having a first polarization state and substantially        reflecting light having an orthogonal second polarization state;        and    -   a first quarter wave retarder at at least one wavelength in the        pre-determined plurality of wavelengths, wherein at least one        chief light ray transmitted through the stop surface and the        image surface passes through the stop surface at an incident        angle of at least 40 degrees.        Embodiment 209 is the optical system of embodiment 208, wherein        the integral optical stack is convex toward the image surface        along orthogonal first and second axes.        Embodiment 210 is the optical system of any of embodiments 208        to 209, wherein substantially any chief light ray having at        least first and second wavelengths at least 150 nm apart in a        visible wavelength range and transmitted through the image        surface and the stop surface has a color separation distance at        the stop surface of less than 1.5 percent of a field of view at        the stop surface.        Embodiment 211 is the optical system of any of embodiments 208        to 210, wherein the color separation distance at the stop        surface is less than 1.2 percent of the field of view at the        stop surface.        Embodiment 212 is the optical system of any of embodiments 208        to 211, wherein substantially any chief light ray having at        least first and second wavelengths at least 150 nm apart in a        visible wavelength range and transmitted through the image        surface and the stop surface has a color separation distance at        the stop surface of less than 20 arc minutes.        Embodiment 213 is the optical system of any of embodiments 208        to 212, wherein the color separation distance at the stop        surface is less than 10 arc minutes.        Embodiment 214 is the optical system of any of embodiments 208        to 213, wherein an image source comprises the image surface and        the stop surface is an exit pupil.        Embodiment 215 is the optical system of embodiment 214, wherein        the image source comprises a display panel.        Embodiment 216 is the optical system of embodiment 215, wherein        the display panel is transparent or semi-transparent.        Embodiment 217 is the optical system of any of embodiments 214        to 216, wherein the image source comprises a shutter.        Embodiment 218 is the optical system of embodiment 208, wherein        the image source comprises an aperture adapted to receive light        reflected from objects external to the optical system.        Embodiment 219 is the optical system of any of embodiments 208        to 213, wherein an image recorder comprises the image surface        and the stop surface is an entrance pupil.        Embodiment 220 is the optical system of any of embodiments 208        to 219, wherein the optical system is centered on a folded        optical axis defined by an optical path of a central light ray        transmitted through the image surface.        Embodiment 221 is the optical system of embodiment 208, wherein        the stop surface is adapted to overlap an entrance pupil of a        second optical system.        Embodiment 222 is the optical system of embodiment 221, wherein        the second optical system is adapted to record images received        at the entrance pupil.        Embodiment 223 is the optical system of embodiment 208, wherein        the stop surface is adapted to overlap an entrance pupil of a        viewer's eye.        Embodiment 224 is the optical system of embodiment 208, wherein        an image source comprises the image surface, the image source        emitting unpolarized light.        Embodiment 225 is the optical system of any of embodiments 208        to 224 further comprising a second quarter wave retarder at at        least one wavelength in the pre-determined plurality of        wavelengths, the second quarter wave retarder disposed between        the partial reflector and the image surface, the first quarter        wave retarder disposed between the multilayer reflective        polarizer and the partial reflector.        Embodiment 226 is the optical system of embodiment 208, wherein        an image source comprises the image surface, the image source        emitting polarized light.        Embodiment 227 is the optical system of embodiment 226, wherein        the polarized light is linearly polarized.        Embodiment 228 is the optical system of embodiment 226, wherein        the polarized light is circularly polarized.        Embodiment 229 is the optical system of embodiment 226, wherein        the polarized light is elliptically polarized.        Embodiment 230 is the optical system of any of embodiments 208        to 229, wherein the partial reflector is a second reflective        polarizer.        Embodiment 231 is the optical system of any of embodiments 208        to 230, wherein the partial reflector has an average optical        transmittance of at least 30% in the pre-determined plurality of        wavelengths.        Embodiment 232 is the optical system of any of embodiments 208        to 231, wherein the pre-determined plurality of wavelengths        comprise at least one continuous wavelength range.        Embodiment 233 is the optical system of any of embodiments 208        to 232, wherein the pre-determined plurality of wavelengths        comprises a visible range of wavelengths.        Embodiment 234 is the optical system of embodiment 233, wherein        the visible range is from 400 nm to 700 nm.        Embodiment 235 is the optical system of any of embodiments 208        to 234, wherein the pre-determined plurality of wavelengths        comprises an infrared range of wavelengths.        Embodiment 236 is the optical system of any of embodiments 208        to 235, wherein the pre-determined plurality of wavelengths        comprises one or more of infrared, visible and ultraviolet        wavelengths.        Embodiment 237 is the optical system of any of embodiments 208        to 236, wherein the partial reflector is a notch reflector.        Embodiment 238 is the optical system of embodiment 237, wherein        the pre-determined plurality of wavelengths comprises one or        more continuous wavelength ranges, and wherein at least one of        the continuous wavelength ranges has a full width at half        maximum of no more than 100 nm.        Embodiment 239 is the optical system of embodiment 238, wherein        the full width at half maximum is no more than 50 nm.        Embodiment 240 is the optical system of any of embodiments 208        to 239, wherein the multilayer reflective polarizer has at least        one first location having a radial distance, r1, from an optical        axis passing through an apex of the multilayer reflective        polarizer, and a displacement, s1, from a plane perpendicular to        the optical axis at the apex, s1/r1 being at least 0.1.        Embodiment 241 is the optical system of embodiment 240, wherein        s1/r1 is at least 0.2.        Embodiment 242 is the optical system of embodiment 240, wherein        s1/r1 is in a range of 0.2 to 0.8.        Embodiment 243 is the optical system of embodiment 240, wherein        s1/r1 is in a range of 0.3 to 0.6.        Embodiment 244 is the optical system of embodiment 240, wherein        the multilayer reflective polarizer has a second location having        a radial distance, r2, from the optical axis and a displacement,        s2, from the plane, s2/r2 being at least 0.3.        Embodiment 245 is the optical system of any of embodiments 208        to 244, wherein the multilayer reflective polarizer has at least        one first location having a radial distance, r1, from an optical        axis passing through an apex of the multilayer reflective        polarizer and a displacement, s1, from a plane perpendicular to        the optical axis at the apex, s1/r1 being at least 0.2, and        wherein for an area of the reflective polarizer defined by s1        and r1, a maximum variation of a transmission axis of the        reflective polarizer is less than about 2 degrees.        Embodiment 246 is the optical system of embodiment 245, wherein        the maximum variation of the transmission axis of the reflective        polarizer is less than about 1.5 degrees.        Embodiment 247 is the optical system of any of embodiments 208        to 246, wherein a maximum variation of a transmission axis of        the reflective polarizer in a reflection aperture of the        reflective polarizer is less than about 1.5 degrees.        Embodiment 248 is the optical system of any of embodiments 209        to 246, wherein a maximum variation of a transmission axis of        the reflective polarizer in a reflection aperture of the        reflective polarizer is less than about 1 degree.        Embodiment 249 is the optical system of any of embodiments 208        to 248, wherein the multilayer reflective polarizer comprises at        least one layer that is substantially optically biaxial at at        least one first location on the at least one layer away from an        optical axis of the second optical stack and substantially        optically uniaxial at at least one second location away from the        optical axis.        Embodiment 250 is the optical system of any of embodiments 208        to 249, wherein the multilayer reflective polarizer is a        thermoformed multilayer reflective polarizer substantially        rotationally symmetric about an optical axis of the second        optical stack.        Embodiment 251 is the optical system of any of embodiments 208        to 250, wherein the multilayer reflective polarizer is a        thermoformed multilayer reflective polarizer rotationally        symmetric about an optical axis of the second optical stack.        Embodiment 252 is the optical system of any of embodiments 208        to 251, wherein substantially any chief light ray that passes        through the image surface and the stop surface is incident on        each of the partial reflector, the multilayer reflective        polarizer, and the first quarter wave retarder with an angle of        incidence less than about 25 degrees.        Embodiment 253 is the optical system of embodiment 208, wherein        an image source comprises the image surface, the image source        emitting an undistorted image, the partial reflector having a        first shape, and the reflective polarizer having a different        second shape such that a distortion of the emitted undistorted        image transmitted by the stop surface is less than about 10% of        a field of view at the stop surface.        Embodiment 254 is the optical system of embodiment 253, wherein        the distortion of the emitted undistorted image transmitted by        the stop surface is less than about 5% of a field of view at the        stop surface.        Embodiment 255 is the optical system of embodiment 253, wherein        the distortion of the emitted undistorted image transmitted by        the stop surface is less than about 3% of a field of view at the        stop surface.        Embodiment 256 is the optical system of any of embodiments 208        to 255, wherein the partial reflector has a first shape, the        multilayer reflective polarizer has a second shape, and one or        both of the first and second shapes is described by an aspheric        polynomial sag equation.        Embodiment 257 is the optical system of any of embodiments 208        to 256, wherein the multilayer reflective polarizer comprises        alternating polymeric layers.        Embodiment 258 is the optical system of any of embodiments 208        to 257, wherein the multilayer reflective polarizer is        thermoformed APF.        Embodiment 259 is the optical system of any of embodiments 208        to 257, wherein the multilayer reflective polarizer comprises a        wire grid polarizer.        Embodiment 260 is the optical system of any of embodiments 208        to 259, wherein the multilayer reflective polarizer is        rotationally symmetric.        Embodiment 261 is the optical system of any of embodiments 208        to 260, wherein the integral optical stack comprises a second        optical lens.        Embodiment 262 is the optical system of embodiment 261, wherein        the first quarter wave retarder is disposed between the first        and second optical lenses.        Embodiment 263 is the optical system of embodiment 261 or 262,        wherein the multilayer reflective polarizer is disposed on a        major surface of second optical lens facing the stop surface and        the partial reflector is disposed on a major surface of the        first optical lens facing the image surface.        Embodiment 264 is an optical system, comprising:-   an image surface;-   a substantially planar stop surface; and-   disposed between the image surface and the stop surface:    -   first, second and third optical lenses;    -   a partial reflector having an average optical reflectance of at        least 30% in a pre-determined plurality of wavelengths;    -   a multilayer reflective polarizer substantially transmitting        light having a first polarization state and substantially        reflecting light having an orthogonal second polarization state;        and    -   a first quarter wave retarder at at least one wavelength in the        pre-determined plurality of wavelengths,-   wherein the optical system comprises a plurality of major surfaces    disposed between the image surface and the stop surface, each major    surface convex toward the image surface along orthogonal first and    second axes, wherein at least six different major surfaces have six    different convexities.    Embodiment 265 is the optical system of embodiment 264, wherein the    plurality of major surfaces includes opposing first and second major    surfaces of the first optical lens, opposing first and second major    surfaces of the second optical lens, and opposing first and second    major surfaces of the third optical lens, each first major surface    facing the stop surface and each second major surface facing the    image surface.    Embodiment 266 is the optical system of embodiment 265, wherein the    second optical lens is disposed between the first and third optical    lenses, and the third optical lens is disposed between the stop    surface and the first optical lens.    Embodiment 267 is the optical system of embodiment 266, wherein the    partial reflector is disposed on the first major surface of the    second optical lens.    Embodiment 268 is the optical system of embodiment 266 or 267,    wherein the multilayer reflective polarizer is disposed on the    second major surface of the third optical lens.    Embodiment 269 is the optical system of embodiment 268, wherein the    first quarter wave retarder is disposed on the multilayer reflective    polarizer.    Embodiment 270 is the optical system of any of embodiments 266 to    269, further comprising a second quarter wave retarder at at least    one wavelength in the pre-determined plurality of wavelengths, the    second quarter wave retarder disposed on the second major surface of    the second optical lens.    Embodiment 271 is the optical system of embodiment 265, wherein the    reflective polarizer is disposed on the first major surface of the    third optical lens and the first quarter wave retarder is disposed    on the second major surface of the third optical lens.    Embodiment 272 is the optical system of embodiment 271, wherein the    partial reflector is disposed on the first or second major surface    of the second optical lens.    Embodiment 273 is the optical system of any of embodiments 264 to    272, wherein an image source comprises the image surface and the    stop surface is an exit pupil.    Embodiment 274 is the optical system of embodiment 273, wherein the    image source comprises a display panel.    Embodiment 275 is the optical system of embodiment 274, wherein the    display panel is substantially transparent.    Embodiment 276 is the optical system of any of embodiments 273 to    275, wherein the image source comprises a shutter.    Embodiment 277 is the optical system of any of embodiments 264 to    272, wherein an image recorder comprises the image surface and the    stop surface is an entrance pupil.    Embodiment 278 is the optical system of any of embodiments 264 to    277, wherein the optical system is centered on a folded optical axis    defined by an optical path of a central light ray transmitted    through the image surface.    Embodiment 279 is the optical system of any of embodiments 264 to    278, wherein the stop surface is adapted to overlap an entrance    pupil of a second optical system.    Embodiment 280 is the optical system of embodiment 279, wherein the    second optical system is adapted to record images received at the    entrance pupil.    Embodiment 281 is the optical system of any of embodiments 264 to    272, wherein the stop surface is adapted to overlap an entrance    pupil of a viewer's eye.    Embodiment 282 is the optical system of any of embodiments 264 to    272, wherein an image source comprises the image surface, the image    source emitting unpolarized light.    Embodiment 283 is the optical system of any of embodiments 264 to    269, wherein the optical stack system further comprises a second    quarter wave retarder at at least one wavelength in the    pre-determined plurality of wavelengths, the second quarter wave    retarder disposed between the partial reflector and the image    surface, the first quarter wave retarder disposed between the    multilayer reflective polarizer and the partial reflector.    Embodiment 284 is the optical system of any of embodiments 264 to    272, wherein an image source comprises the image surface, the image    source emitting polarized light.    Embodiment 285 is the optical system of embodiment 284, wherein the    polarized light is linearly polarized.    Embodiment 286 is the optical system of embodiment 284, wherein the    polarized light is circularly polarized.    Embodiment 287 is the optical system of embodiment 284, wherein the    polarized light is elliptically polarized.    Embodiment 288 is the optical system of any of embodiments 264 to    287, wherein the partial reflector is a second reflective polarizer.    Embodiment 289 is the optical system of any of embodiments 264 to    288, wherein the partial reflector has an average optical    transmittance of at least 30% in the pre-determined plurality of    wavelengths.    Embodiment 290 is the optical system of any of embodiments 264 to    289, wherein the pre-determined plurality of wavelengths comprise at    least one continuous wavelength range.    Embodiment 291 is the optical system of any of embodiments 264 to    290, wherein the pre-determined plurality of wavelengths comprises a    visible range of wavelengths.    Embodiment 292 is the optical system of embodiment 291, wherein the    visible range is from 400 nm to 700 nm.    Embodiment 293 is the optical system of any of embodiments 264 to    292, wherein the pre-determined plurality of wavelengths comprises    an infrared range of wavelengths.    Embodiment 294 is the optical system of any of embodiments 264 to    293, wherein the pre-determined plurality of wavelengths comprises    one or more of infrared, visible and ultraviolet wavelengths.    Embodiment 295 is the optical system of any of embodiments 264 to    294, wherein the partial reflector is a notch reflector.    Embodiment 296 is the optical system of embodiment 295, wherein the    pre-determined plurality of wavelengths comprises one or more    continuous wavelength ranges, and wherein at least one of the    continuous wavelength ranges has a full width at half maximum of no    more than 100 nm.    Embodiment 297 is the optical system of embodiment 296, wherein the    full width at half maximum is no more than 50 nm.    Embodiment 298 is the optical system of any of embodiments 264 to    297, wherein the multilayer reflective polarizer has at least one    first location having a radial distance, r1, from an optical axis    passing through an apex of the multilayer reflective polarizer, and    a displacement, s1, from a plane perpendicular to the optical axis    at the apex, s1/r1 being at least 0.1.    Embodiment 299 is the optical system of embodiment 298, wherein    s1/r1 is at least 0.2.    Embodiment 300 is the optical system of embodiment 298, wherein    s1/r1 is in a range of 0.2 to 0.8.    Embodiment 301 is the optical system of embodiment 298, wherein    s1/r1 is in a range of 0.3 to 0.6.    Embodiment 302 is the optical system of any of embodiments 298 to    301, wherein the multilayer reflective polarizer has a second    location having a radial distance, r2, from the optical axis and a    displacement, s2, from the plane, s2/r2 being at least 0.3.    Embodiment 303 is the optical system of any of embodiments 264 to    297, wherein the multilayer reflective polarizer has at least one    first location having a radial distance, r1, from an optical axis    passing through an apex of the multilayer reflective polarizer and a    displacement, s1, from a plane perpendicular to the optical axis at    the apex, s1/r1 being at least 0.2, and wherein for an area of the    reflective polarizer defined by s1 and r1, a maximum variation of a    transmission axis of the reflective polarizer is less than about 2    degrees.    Embodiment 304 is the optical system of embodiment 303, wherein the    maximum variation of the transmission axis of the reflective    polarizer is less than about 1.5 degrees.    Embodiment 305 is the optical system of any of embodiments 264 to    304, wherein a maximum variation of a transmission axis of the    reflective polarizer in a reflection aperture of the reflective    polarizer is less than about 1.5 degrees.    Embodiment 306 is the optical system of any of embodiments 264 to    304, wherein a maximum variation of a transmission axis of the    reflective polarizer in a reflection aperture of the reflective    polarizer is less than about 1 degree.    Embodiment 307 is the optical system of any of embodiments 264 to    306, wherein the multilayer reflective polarizer comprises at least    one layer that is substantially optically biaxial at at least one    first location on the at least one layer away from an optical axis    of the second optical stack and substantially optically uniaxial at    at least one second location away from the optical axis.    Embodiment 308 is the optical system of any of embodiments 264 to    307, wherein the multilayer reflective polarizer is a thermoformed    multilayer reflective polarizer substantially rotationally symmetric    about an optical axis of the second optical stack.    Embodiment 309 is the optical system of any of embodiments 264 to    308, wherein the multilayer reflective polarizer is a thermoformed    multilayer reflective polarizer rotationally symmetric about an    optical axis of the second optical stack.    Embodiment 310 is the optical system of any of embodiments 264 to    309, wherein substantially any chief light ray that passes through    the image surface and the stop surface is incident on each of the    partial reflector, the multilayer reflective polarizer, and the    first quarter wave retarder with an angle of incidence less than    about 25 degrees.    Embodiment 311 is the optical system of any of embodiments 264 to    272, wherein an image source comprises the image surface, the image    source emitting an undistorted image, the partial reflector having a    first shape, and the reflective polarizer having a different second    shape such that a distortion of the emitted undistorted image    transmitted by the stop surface is less than about 10% of a field of    view at the stop surface.    Embodiment 312 is the optical system of embodiment 311, wherein the    distortion of the emitted undistorted image transmitted by the stop    surface is less than about 5% of a field of view at the stop    surface.    Embodiment 313 is the optical system of embodiment 311, wherein the    distortion of the emitted undistorted image transmitted by the stop    surface is less than about 3% of a field of view at the stop    surface.    Embodiment 314 is the optical system of any of embodiments 264 to    313, wherein substantially any chief light ray having at least first    and second wavelengths at least 150 nm apart in a visible wavelength    range and emitted by the image surface and transmitted by the stop    surface has a color separation distance at the stop surface of less    than 1.5 percent of a field of view at the stop surface.    Embodiment 315 is the optical system of embodiment 314, wherein the    color separation distance at the stop surface is less than 1.2    percent of the field of view at the stop surface.    Embodiment 316 is the optical system of any of embodiments 264 to    315, wherein substantially any chief light ray having at least first    and second wavelengths at least 150 nm apart in a visible wavelength    range and transmitted through the image surface and the stop surface    has a color separation distance at the stop surface of less than 20    arc minutes.    Embodiment 317 is the optical system of embodiment 316, wherein the    color separation distance at the stop surface is less than 10 arc    minutes.    Embodiment 318 is the optical system of any of embodiments 264 to    249, wherein the partial reflector has a first shape, the multilayer    reflective polarizer has a second shape, and one or both of the    first and second shapes is described by an aspheric polynomial sag    equation.    Embodiment 319 is the optical system of any of embodiments 264 to    318, wherein the multilayer reflective polarizer comprises    alternating polymeric layers.    Embodiment 320 is the optical system of any of embodiments 264 to    319, wherein the multilayer reflective polarizer is thermoformed    APF.    Embodiment 321 is the optical system of any of embodiments 264 to    319, wherein the multilayer reflective polarizer comprises a wire    grid polarizer.    Embodiment 322 is the optical system of any of embodiments 264 to    321, wherein the multilayer reflective polarizer is rotationally    symmetric.    Embodiment 323 is the optical system of any of embodiments 264 to    322, wherein at least one of the first, second and third optical    lenses have a user-adjustable position relative to the stop and    image surfaces.    Embodiment 324 is the optical system of any of embodiments 264 to    323, wherein at least one of the first, second and third optical    lenses have a user-adjustable shape.    Embodiment 325 is the optical system of any of embodiments 264 to    324 wherein the image surface is substantially planar.    Embodiment 326 is the optical system of any of embodiments 264 to    324, wherein the image surface is curved.    Embodiment 327 is the optical system of any of embodiments 1 to 326,    having a contrast ratio at the stop surface of at least 40 over a    field of view of the optical system.    Embodiment 328 is the optical system of any of embodiments 1 to 327,    having a contrast ratio at the stop surface of at least 50 over a    field of view of the optical system.    Embodiment 329 is the optical system of any of embodiments 1 to 328,    having a contrast ratio at the stop surface of at least 60 over a    field of view of the optical system.    Embodiment 330 is the optical system of any of embodiments 1 to 329,    having a contrast ratio at the stop surface of at least 80 over a    field of view of the optical system.    Embodiment 331 is the optical system of any of embodiments 1 to 330,    having a contrast ratio at the stop surface of at least 100 over a    field of view of the optical system.    Embodiment 332 is the optical system of any of embodiments 1 to 333,    wherein at least one lens has a non-uniform edge profile.    Embodiment 333 is the optical system of embodiment 332, wherein the    edge profile comprises a shape adapted to conform to a face when the    optical system is used in a head-mounted display.    Embodiment 334 is a thermoformed multilayer reflective polarizer    substantially rotationally symmetric about an optical axis passing    thorough an apex of the thermoformed multilayer reflective polarizer    and convex along orthogonal first and second axes orthogonal to the    optical axis, the thermoformed multilayer reflective polarizer    having:    -   at least one inner layer substantially optically uniaxial at at        least one first location away from the apex; and    -   at least one first location on the reflective polarizer having a        radial distance, r1, from the optical axis and a displacement,        s1, from a plane perpendicular to the optical axis at the apex,        s1/r1 being at least 0.2.        Embodiment 335 is the thermoformed multilayer reflective        polarizer of embodiment 334, wherein for an area of the        reflective polarizer defined by s1 and r1, a maximum variation        of a transmission axis of the reflective polarizer is less than        about 2 degrees.        Embodiment 336 is the optical system of embodiment 335, wherein        the maximum variation of the transmission axis of the reflective        polarizer is less than about 1.5 degrees.        Embodiment 337 is the optical system of any of embodiments 334        to 336, wherein a maximum variation of a transmission axis of        the reflective polarizer in a reflection aperture of the        reflective polarizer is less than about 1.5 degrees.        Embodiment 338 is the optical system of any of embodiments 334        to 336, wherein a maximum variation of a transmission axis of        the reflective polarizer in a reflection aperture of the        reflective polarizer is less than about 1 degree.        Embodiment 339 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 338, wherein the at least        one inner layer is substantially optically biaxial at at least        one second location on the at least one layer away from the        apex.        Embodiment 340 is a thermoformed multilayer reflective polarizer        substantially rotationally symmetric about an optical axis        passing thorough an apex of the thermoformed multilayer        reflective polarizer and convex along orthogonal first and        second axes orthogonal to the optical axis, the thermoformed        multilayer reflective polarizer having:    -   at least one first location on the reflective polarizer having a        radial distance, r1, from the optical axis and a displacement,        s1, from a plane perpendicular to the optical axis at the apex,        s1/r1 being at least 0.2,    -   wherein for an area of the reflective polarizer defined by s1        and r1, a maximum variation of a transmission axis of the        reflective polarizer is less than about 2 degrees.        Embodiment 341 is the thermoformed multilayer reflective        polarizer of embodiment 340, wherein the maximum variation of        the transmission axis of the reflective polarizer is less than        about 1.5 degrees.        Embodiment 342 is the thermoformed multilayer reflective        polarizer of embodiment 340 or 341 comprising at least one layer        that is substantially optically biaxial at at least one first        location on the at least one layer away from an optical axis of        the reflective polarizer and substantially optically uniaxial at        at least one second location away from the optical axis.        Embodiment 343 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 342, wherein s1/r1 is        less than about 0.8.        Embodiment 344 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 343, wherein the        reflective polarizer has a second location having a radial        distance, r2, from the optical axis and a displacement, s2, from        the plane, s2/r2 being at least 0.3.        Embodiment 345 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 344, wherein an azimuthal        variation in s1/r1 is less than 10 percent.        Embodiment 346 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 344, wherein an azimuthal        variation in s1/r1 is less than 8 percent.        Embodiment 347 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 344, wherein an azimuthal        variation in s1/r1 is less than 6 percent.        Embodiment 348 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 344, wherein an azimuthal        variation in s1/r1 is less than 4 percent.        Embodiment 349 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 344, wherein an azimuthal        variation in s1/r1 is less than 2 percent.        Embodiment 350 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 344, wherein an azimuthal        variation in s1/r1 is less than 1 percent.        Embodiment 351 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 350 comprising        alternating polymeric layers.        Embodiment 352 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 351 being thermoformed        APF.        Embodiment 353 is the thermoformed multilayer reflective        polarizer of any of embodiments 334 to 351 comprising a wire        grid polarizer.        Embodiment 354 is a lens having a surface curved about two        orthogonal directions, and comprising the thermoformed        multilayer reflective polarizer of any of embodiments 334 to 353        disposed on the surface.        Embodiment 355 is an optical stack comprising:-   a first lens;-   a second lens adjacent the first lens;-   a quarter wave retarder disposed between the first and second    lenses;-   a reflective polarizer disposed on the second lens opposite the    first lens; and-   a partial reflector disposed on the first lens opposite the second    lens,-   wherein the reflective polarizer is curved about two orthogonal    axes, and wherein the optical stack is an integral optical stack.    Embodiment 356 is the optical sack of embodiment 355, wherein the    first lens comprises a first material and the second lens comprises    a second material.    Embodiment 357 is the optical stack of embodiment 356, wherein the    first and second materials are the same.    Embodiment 358 is the optical stack of embodiment 356, wherein the    first and second materials are different.    Embodiment 359 is the optical stack of embodiment 355, wherein at    least one of the first and second materials is a polymer.    Embodiment 360 is the optical stack of embodiment 359, wherein the    first material is a first polymer and the second material is a    second polymer.    Embodiment 361 is the optical stack of embodiment 360, wherein the    first and second polymers are different.    Embodiment 362 is the optical stack of any one of embodiments 355,    or 356, or 358 to 361, wherein the first and second lenses have    different Abbe numbers.    Embodiment 363 is the optical stack of embodiment 362, wherein a    difference in the Abbe numbers of the first and second lenses is in    a range of 5 to 50.    Embodiment 364 is the optical stack of any of embodiments 355 to    363, wherein one of the first and second lenses has an Abbe number    greater than 45 and the other of the first and second lenses has an    Abbe number less than 45.    Embodiment 365 is the optical stack of any of embodiments 355 to    364, wherein one of the first and second lenses has an Abbe number    greater than 50 and the other of the first and second lenses has an    Abbe number less than 40.    Embodiment 366 is the optical stack of any of embodiments 355 to    365, wherein the reflective polarizer is the thermoformed multilayer    reflective polarizer of any of embodiments 334 to 353.    Embodiment 367 is the optical stack of any of embodiments 355 to    366, wherein the partial reflector has an average an average optical    reflectance of at least 30% in a desired plurality of wavelengths.    Embodiment 368 is the optical stack of any of embodiments 355 to    367, wherein the partial reflector has an average an average optical    transmittance of at least 30% in a desired plurality of wavelengths.    Embodiment 369 is the optical stack of any of embodiments 355 to    368, wherein the partial reflector is a reflective polarizer.    Embodiment 370 is the optical stack of any of embodiments 355 to    369, wherein the desired plurality of wavelengths comprise at least    one continuous wavelength range.    Embodiment 371 is the optical stack of any of embodiments 355 to    370, wherein the desired plurality of wavelengths comprises a    visible range of wavelengths.    Embodiment 372 is the optical stack of embodiment 371, wherein the    visible range is from 400 nm to 700 nm.    Embodiment 373 is the optical stack of any of embodiments 355 to    372, wherein the desired plurality of wavelengths comprises an    infrared range of wavelengths.    Embodiment 374 is the optical stack of any of embodiments 355 to    373, wherein the desired plurality of wavelengths comprises one or    more of infrared, visible and ultraviolet wavelengths.    Embodiment 375 is the optical stack of any of embodiments 355 to    374, wherein the partial reflector is a notch reflector.    Embodiment 376 is the optical stack of any of embodiments 355 to    375, wherein the desired plurality of wavelengths comprises one or    more continuous wavelength ranges, and wherein at least one of the    continuous wavelength ranges has a full width at half maximum of no    more than 100 nm.    Embodiment 377 is the optical stack of any of embodiments 355 to    376, wherein the full width at half maximum is no more than 50 nm.    Embodiment 378 is an optical system comprising an image surface, a    stop surface, and the optical stack of any of embodiments 355 to 376    disposed between the image surface and the stop surface.    Embodiment 379 is an optical system comprising an image surface, a    stop surface, and the thermoformed multilayer reflective polarizer    of any of embodiments 334 to 353 disposed between the image surface    and the stop surface.    Embodiment 380 is the optical system of embodiment 379 further    comprising:-   a quarter wave retarder disposed between the image surface and the    reflective polarizer; and a partial reflector disposed between the    image surface and the quarter wave retarder.    Embodiment 381 is the optical system of any of embodiments 1 to 333,    wherein the reflective polarizer is a thermoformed multilayer    reflective polarizer according to any of embodiments 334 to 353.    Embodiment 382 is a method of making an optical stack, comprising:-   providing a thermoform tool centered on a tool axis and having an    external surface rotationally asymmetric about the tool axis;-   heating an optical film resulting in a softened optical film;-   conforming the softened optical film to the external surface while    stretching the softened film along at least orthogonal first and    second directions away from the tool axis resulting in a conformed    optical film rotationally asymmetric about an optical axis of the    conformed film, the optical axis coincident with the tool axis;-   cooling the conformed optical film resulting in a symmetric optical    film rotationally symmetric about the optical axis; and-   molding an optical lens on the symmetric optical film resulting in    the optical stack.    Embodiment 383 is the method of embodiment 382, wherein the cooling    step further comprises releasing the optical film from the tool.    Embodiment 384 is the method of embodiment 382 or 383, wherein the    molding an optical lens step includes molding a second film onto the    optical lens opposite the optical film.    Embodiment 385 is the method of embodiment 384, wherein the second    film comprises a partial reflector.    Embodiment 386 is the method of any of embodiments 382 to 385,    wherein the optical film comprises a reflective polarizer.    Embodiment 387 is the method of embodiment 386, wherein the optical    film further comprises a quarter wave retarder.    Embodiment 388 is the method of embodiment 386 or 387, wherein the    reflective polarizer is a multilayer polymeric reflective polarizer.    Embodiment 389 is the method of embodiment 388, wherein the    reflective polarizer is APF.    Embodiment 390 is the method of embodiment 386 or 387, wherein the    reflective polarizer is a wire grid polarizer.    Embodiment 391 is a method of making a desired optical film having a    desired shape, comprising: providing a thermoform tool having an    external surface having a first shape different than the desired    shape;-   heating an optical film resulting in a softened optical film;-   conforming the softened optical film to the external surface having    the first shape while stretching the softened film along at least    orthogonal first and second directions resulting in a conformed    optical film having the first shape; and-   cooling the conformed optical film resulting in the desired optical    film having the desired shape.    Embodiment 392 is the method of embodiment 391, wherein the cooling    step further comprises releasing the conformed optical film from the    tool.    Embodiment 393 is the method of any of embodiments 391 or 392,    wherein the desired shape is rotationally symmetric about an optical    axis of the desired optical film.    Embodiment 394 is the method of any of embodiments 391 to 393,    wherein the thermoform tool is centered on a tool axis and the    external surface is rotationally asymmetric about the tool axis.    Embodiment 395 is the method of any of embodiments 391 to 393,    further comprising molding an optical lens on the desired optical    film resulting in an optical stack.    Embodiment 396 is the method of embodiment 395, wherein the molding    an optical lens step includes molding a second film on the optical    lens opposite the desired optical film.    Embodiment 397 is the method of embodiment 396, wherein the second    film comprises a partial reflector.    Embodiment 398 is the method of any of embodiments 391 to 397,    wherein the desired optical film comprises a reflective polarizer.    Embodiment 399 is the method of embodiment 398, wherein the desired    optical film further comprises a quarter wave retarder.    Embodiment 400 is the method of embodiment 398 or 399, wherein the    reflective polarizer is a multilayer polymeric reflective polarizer.    Embodiment 401 is the method of embodiment 400, wherein the    reflective polarizer is APF.    Embodiment 402 is the method of embodiment 398 or 399, wherein the    reflective polarizer is a wire grid polarizer.    Embodiment 403 is an optical system, comprising:-   an image surface;-   a stop surface;-   a first optical stack disposed between the image surface and the    stop surface and comprising:    -   a first optical lens;    -   a partial reflector having an average optical reflectance of at        least 30% in a desired plurality of wavelengths; and-   a second optical stack disposed between the first optical stack and    the stop surface and comprising:    -   a second optical lens;    -   a thermoformed multilayer reflective polarizer rotationally        symmetric about an optical axis of the second optical stack and        convex toward the image surface along orthogonal first and        second axes orthogonal to the optical axis, the thermoformed        multilayer reflective polarizer having at least one first        location having a radial distance, r1, from an optical axis        passing through an apex of the thermoformed multilayer        reflective polarizer, and a displacement, s1, from a plane        perpendicular to the optical axis at the apex, s1/r1 being at        least 0.1; and    -   a first quarter wave retarder disposed between the reflective        polarizer and the first optical stack.        Embodiment 404 is the optical system of embodiment 403, wherein        an image source comprises the image surface and the stop surface        is an exit pupil.        Embodiment 405 is the optical system of embodiment 404, wherein        the image source comprises a display panel.        Embodiment 406 is the optical system of embodiment 405, wherein        the display panel is transparent or semi-transparent.        Embodiment 407 is the optical system of any of embodiments 404        to 406, wherein the image source comprises a shutter.        Embodiment 408 is the optical system of embodiment 403, wherein        the image source comprises an aperture adapted to receive light        reflected from objects external to the optical system.        Embodiment 409 is the optical system of embodiment 403, wherein        an image recorder comprises the image surface and the stop        surface is an entrance pupil.        Embodiment 410 is the optical system of any of embodiments 403        to 409, wherein the optical system is centered on a folded        optical axis defined by an optical path of a central light ray        transmitted through the image surface.        Embodiment 411 is the optical system of any of embodiments 403        to 410, wherein the stop surface is adapted to overlap an        entrance pupil of a second optical system.        Embodiment 412 is the optical system of embodiment 411, wherein        the second optical system is adapted to record images received        at the entrance pupil.        Embodiment 413 is the optical system of embodiment 403, wherein        the stop surface is adapted to overlap an entrance pupil of a        viewer's eye.        Embodiment 414 is the optical system of embodiment 403, wherein        an image source comprises the image surface, the image source        emitting unpolarized light.        Embodiment 415 is the optical system of any of embodiments 403        to 414, wherein the first optical stack further comprises a        second quarter wave retarder disposed between the partial        reflector and the image surface.        Embodiment 416 is the optical system of embodiment 403, wherein        an image source comprises the image surface, the image source        emitting polarized light.        Embodiment 417 is the optical system of embodiment 416, wherein        the polarized light is linearly polarized.        Embodiment 418 is the optical system of embodiment 416, wherein        the polarized light is circularly polarized.        Embodiment 419 is the optical system of embodiment 416, wherein        the polarized light is elliptically polarized.        Embodiment 420 is the optical system of any of embodiments 403        to 419, wherein the partial reflector is a second reflective        polarizer.        Embodiment 421 is the optical system of any of embodiments 403        to 420, wherein the partial reflector has an average optical        transmittance of at least 30% in the desired plurality of        wavelengths.        Embodiment 422 is the optical system of any of embodiments 403        to 421, wherein the desired plurality of wavelengths comprise at        least one continuous wavelength range.        Embodiment 423 is the optical system of any of embodiments 403        to 422, wherein the desired plurality of wavelengths comprises a        visible range of wavelengths.        Embodiment 424 is the optical system of embodiment 423, wherein        the visible range is from 400 nm to 700 nm.        Embodiment 425 is the optical system of any of embodiments 403        to 424, wherein the desired plurality of wavelengths comprises        an infrared range of wavelengths.        Embodiment 426 is the optical system of any of embodiments 403        to 425, wherein the desired plurality of wavelengths comprises        one or more of infrared, visible and ultraviolet wavelengths.        Embodiment 427 is the optical system of any of embodiments 403        to 426, wherein the partial reflector is a notch reflector.        Embodiment 428 is the optical system of embodiment 427, wherein        the desired plurality of wavelengths comprises one or more        continuous wavelength ranges, and wherein at least one of the        continuous wavelength ranges has a full width at half maximum of        no more than 100 nm.        Embodiment 429 is the optical system of embodiment 428, wherein        the full width at half maximum is no more than 50 nm.        Embodiment 430 is the optical system of any of embodiments 403        to 429, wherein s1/r1 is at least 0.2.        Embodiment 431 is the optical system of any of embodiments 403        to 430, wherein s1/r1 is in a range of 0.2 to 0.8.        Embodiment 432 is the optical system any of embodiments 403 to        431, wherein s1/r1 is in a range of 0.3 to 0.6.        Embodiment 433 is the optical system of any of embodiments 424        to 432, wherein the multilayer reflective polarizer has a second        location having a radial distance, r2, from the optical axis and        a displacement, s2, from the plane, s2/r2 being at least 0.3.        Embodiment 434 is the optical system of any of embodiments 403        to 433, wherein for an area of the reflective polarizer defined        by s1 and r1, a maximum variation of a transmission axis of the        reflective polarizer is less than about 2 degrees.        Embodiment 435 is the optical system of any of embodiments 403        to 433, wherein for an area of the reflective polarizer defined        by s1 and r1, a maximum variation of a transmission axis of the        reflective polarizer is less than about 1.5 degrees.        Embodiment 436 is the optical system of any of embodiments 403        to 433, wherein for an area of the reflective polarizer defined        by s1 and r1, a maximum variation of a transmission axis of the        reflective polarizer is less than about 1 degree.        Embodiment 437 is the optical system of any of embodiments 403        to 436, wherein the first optical lens has a first major surface        facing the second optical lens and an opposing second major        surface facing the image surface, and the second optical lens        has a first major surface facing the stop surface and an        opposing second major surface facing the first optical lens.        Embodiment 438 is the optical system of embodiment 437, wherein        the partial reflector is disposed on the first or second major        surface of the first lens.        Embodiment 439 is the optical system of embodiment 437, wherein        the partial reflector is disposed on the first major surface of        the first lens and a second quarter wave retarder is disposed on        the second major surface of the first lens.        Embodiment 440 is the optical system of embodiment 437, wherein        the partial reflector is disposed on the second major surface of        the first lens and a second quarter wave retarder is disposed on        the partial reflector opposite the second major surface of the        first lens.        Embodiment 441 is the optical system of embodiment 437, wherein        a second quarter wave retarder is disposed on the first major        surface of the first optical lens and the partial reflector is        disposed on the second quarter wave retarder opposite the first        major surface of the first optical lens.        Embodiment 442 is the optical system of embodiment 437, wherein        the first quarter wave retarder is disposed on the second major        surface of the second optical lens and the multilayer reflective        polarizer is disposed on the first major surface of the second        optical lens.        Embodiment 443 is the optical system of embodiment 437, wherein        the multilayer reflective polarizer is disposed on the second        major surface of the second optical lens and the first quarter        wave retarder is disposed on the multilayer reflective polarizer        opposite the second major surface of the second optical lens.        Embodiment 444 is the optical system of any of embodiments 403        to 443, wherein the multilayer reflective polarizer comprises at        least one layer that is substantially optically biaxial at at        least one first location on the at least one layer away from an        optical axis of the second optical stack and substantially        optically uniaxial at at least one second location away from the        optical axis.        Embodiment 445 is the optical system of any of embodiments 403        to 444, wherein substantially any chief light ray that passes        through the image surface and the stop surface is incident on        each of the first optical stack and the second optical stack        with an angle of incidence less than about 25 degrees.        Embodiment 446 is the optical system of any of embodiments 403        to 445, wherein the first and second optical stacks have a        substantially same shape.        Embodiment 447 is the optical system of any of embodiments 403        to 445, wherein the first and second optical stacks have        different shapes.        Embodiment 448 is the optical system of any of embodiments 403        to 447, wherein each of the first and second lenses are plano        lenses.        Embodiment 449 is the optical system of any of embodiments 403        to 448, wherein the first and second optical lenses have a        substantially same shape.        Embodiment 450 is the optical system of any of embodiments 403        to 448, wherein the first and second optical lenses have        different shapes.        Embodiment 451 is the optical system of any of embodiments 403        to 450, wherein the image surface is substantially planar.        Embodiment 452 is the optical system of any of embodiments 403        to 450, wherein the image surface is substantially curved.        Embodiment 453 is the optical system of embodiment 403, wherein        an image source comprises the image surface, the image source        emitting an undistorted image, the partial reflector having a        first shape, and the reflective polarizer having a different        second shape such that a distortion of the emitted undistorted        image transmitted by the stop surface is less than about 10% of        a field of view at the stop surface.        Embodiment 454 is the optical system of embodiment 453, wherein        the distortion of the emitted undistorted image transmitted by        the stop surface is less than about 5% of a field of view at the        stop surface.        Embodiment 455 is the optical system of embodiment 453, wherein        the distortion of the emitted undistorted image transmitted by        the stop surface is less than about 3% of a field of view at the        stop surface.        Embodiment 456 is the optical system of any of embodiments 403        to 455, wherein substantially any chief light ray having at        least first and second wavelengths at least 150 nm apart in a        visible wavelength range and transmitted through the image        surface and the stop surface has a color separation distance at        the stop surface of less than 1.5 percent of a field of view at        the stop surface.        Embodiment 457 is the optical system of embodiment 456, wherein        the color separation distance at the stop surface is less than        1.2 percent of the field of view at the stop surface.        Embodiment 458 is the optical system of any of embodiments 403        to 457, wherein substantially any chief light ray having at        least first and second wavelengths at least 150 nm apart in a        visible wavelength range and transmitted through the image        surface and the stop surface has a color separation distance at        the stop surface of less than 20 arc minutes.        Embodiment 459 is the optical system of embodiment 458, wherein        the color separation distance at the stop surface is less than        10 arc minutes.        Embodiment 460 is the optical system of any of embodiments 403        to 459, wherein the partial reflector has a first shape, the        multilayer reflective polarizer has a second shape, and one or        both of the first and second shapes is described by an aspheric        polynomial sag equation.        Embodiment 461 is the optical system of any of embodiments 403        to 460, wherein the multilayer reflective polarizer comprises        alternating polymeric layers.        Embodiment 462 is the optical system of any of embodiments 403        to 461, wherein the multilayer reflective polarizer is        thermoformed APF.        Embodiment 463 is the optical system of any of embodiments 403        to 461, wherein the multilayer reflective polarizer comprises a        wire grid polarizer.        Embodiment 464 is the optical system of any of embodiments 403        to 463, wherein at least one of the first and second optical        stacks have an adjustable position relative to the stop and        image surfaces.        Embodiment 465 is the optical system of any of embodiments 403        to 464, wherein the first optical stack has an adjustable shape.        Embodiment 466 is an optical system, comprising:-   a partial reflector having an average optical reflectance of at    least 30% in a desired plurality of wavelengths; and-   a multilayer reflective polarizer substantially transmitting light    having a first polarization state and substantially reflecting light    having an orthogonal second polarization state, the multilayer    reflective polarizer convex along orthogonal first and second axes,    at least one first location on the multilayer reflective polarizer    having a radial distance r1 from an optical axis of the multilayer    reflective polarizer and a displacement s1 from a plane    perpendicular to the optical axis at an apex of the multilayer    reflective polarizer, s1/r1 being at least 0.1; and-   a first quarter wave retarder disposed between the partial reflector    and the multilayer reflective polarizer,-   wherein the multilayer reflective polarizer comprises at least one    layer substantially optically biaxial at at least one first location    on the at least one layer away from the optical axis and    substantially optically uniaxial at at least one second location    away from the optical axis.    Embodiment 467 is the optical system of embodiment 466, wherein the    multilayer reflective polarizer is disposed adjacent to and spaced    apart from the partial reflector.    Embodiment 468 is the optical system of embodiment 466 or embodiment    467, wherein a first optical stack comprises a first optical lens    and the partial reflector.    Embodiment 469 is the optical system of any of embodiments 466 to    468, where a second optical stack comprises a second optical lens    and the multilayer reflective polarizer.    Embodiment 470 is an optical system, comprising:-   a first optical stack, the first optical stack comprising:    -   a first optical lens; and    -   a partial reflector having an average optical reflectance of at        least 30% in a desired plurality of wavelengths; and-   a second optical stack disposed adjacent to the first optical stack    and convex along orthogonal first and second axes, the second    optical stack comprising:    -   a second optical lens;    -   a multilayer reflective polarizer substantially transmitting        light having a first polarization state and substantially        reflecting light having an orthogonal second polarization state,        at least one first location on the multilayer reflective        polarizer having a radial distance r1 from an optical axis of        the second optical stack and a displacement s1 from a plane        perpendicular to the optical axis at an apex of the multilayer        reflective polarizer, s1/r1 being at least 0.1; and-   a first quarter wave retarder disposed between the second optical    stack and the first optical stack, wherein the multilayer reflective    polarizer comprises at least one layer substantially optically    biaxial at at least one first location on the at least one layer    away from the optical axis and substantially optically uniaxial at    at least one second location away from the optical axis.    Embodiment 471 is an optical system, comprising:-   a first optical stack, the first optical stack comprising:    -   a first optical lens; and    -   a partial reflector having an average optical reflectance of at        least 30% in a desired plurality of wavelengths; and-   a second optical stack disposed adjacent to the first optical stack    and convex along orthogonal first and second axes, the second    optical stack comprising:    -   a second optical lens;    -   a reflective polarizer substantially transmitting light having a        first polarization state and substantially reflecting light        having an orthogonal second polarization state, at least one        first location on the reflective polarizer having a radial        distance r1 from an optical axis of the second optical stack and        a displacement s1 from a plane perpendicular to the optical axis        at an apex of the reflective polarizer, s1/r1 being at least        0.1; and-   a first quarter wave retarder disposed between the second optical    stack and the first optical stack, wherein the optical system has a    contrast ratio of at least 50 over a field of view of the optical    system.    Embodiment 472 is the optical system of embodiment 471, wherein the    contrast ratio is at least 60.    Embodiment 473 is the optical system of embodiment 471, wherein the    contrast ratio is at least 80.    Embodiment 474 is the optical system of embodiment 471, wherein the    contrast ratio is at least 100.    Embodiment 475 is the optical system of any of embodiments 469 to    474, wherein the second optical stack is spaced apart from the first    optical stack.    Embodiment 476 is an optical system, comprising:-   a first optical stack, the first optical stack comprising:    -   a first optical lens; and    -   a partial reflector having an average optical reflectance of at        least 30% in a desired plurality of wavelengths; and-   a second optical stack disposed adjacent to the first optical stack    and convex along orthogonal first and second axes, the second    optical stack comprising:    -   a second optical lens;    -   a reflective polarizer substantially transmitting light having a        first polarization state and substantially reflecting light        having an orthogonal second polarization state, at least one        first location on the reflective polarizer having a radial        distance r1 from an optical axis of the second optical stack and        a displacement s1 from a plane perpendicular to the optical axis        at an apex of the reflective polarizer, s being at least 0.1;        and-   a first quarter wave retarder disposed between the second optical    stack and the first optical stack, wherein the optical system is    adapted to provide an adjustable dioptric correction.    Embodiment 477 is the optical system of any of embodiments 466 to    476, wherein the reflective polarizer comprises at least one layer    substantially optically biaxial at at least one first location on    the at least one layer away from the optical axis and substantially    optically uniaxial at at least one second location away from the    optical axis.    Embodiment 478 is the optical system of any of embodiments 466 to    476, wherein the reflective polarizer is a wire grid polarizer.    Embodiment 479 is the optical system of embodiment 476, wherein the    adjustable dioptric correction is provided by one or more of an    adjustable distance between the first and second optical stacks, an    adjustable shape of the first optical stack, and an adjustable shape    of the second optical stack.    Embodiment 480 is the optical system of any of embodiments 466 to    479, further comprising an image surface and a stop surface, the    partial reflector disposed between the image surface and the stop    surface, the reflective polarizer disposed between the partial    reflector and the stop surface.    Embodiment 481 is the optical system of embodiment 480, wherein the    reflective polarizer is convex toward the image surface about the    orthogonal first and second axes.    Embodiment 482 is the optical system of embodiment 480 or 481,    wherein the partial reflector is convex toward the image surface    about the orthogonal first and second axes.    Embodiment 483 is the optical system of any of embodiments 480 to    482, wherein substantially any chief light ray that passes through    the image surface and the stop surface is incident on each of the    partial reflector and the reflective polarizer with an angle of    incidence less than about 30 degrees.    Embodiment 484 is the optical system of any of embodiments 480 to    482, wherein substantially any chief light ray that passes through    the image surface and the stop surface is incident on each of the    partial reflector and the reflective polarizer with an angle of    incidence less than about 25 degrees.    Embodiment 485 is the optical system of any of embodiments 466 to    477, or embodiments 479 to 482, wherein the reflective polarizer is    APF.    Embodiment 486 is the optical system of any of embodiments 466 to    477, or embodiments 479 to 485, wherein the reflective polarizer is    thermoformed APF.    Embodiment 487 is the optical system of any of embodiments 466 to    486, wherein the partial reflector is a second reflective polarizer.    Embodiment 488 is the optical system of any of embodiments 466 to    487, wherein the partial reflector has an average optical    transmittance of at least 30% in the desired plurality of    wavelengths.    Embodiment 489 is the optical system of any of embodiments 466 to    488, wherein the desired plurality of wavelengths comprise at least    one continuous wavelength range.    Embodiment 490 is the optical system of any of embodiments 466 to    489, wherein the desired plurality of wavelengths comprises a    visible range of wavelengths.    Embodiment 491 is the optical system of embodiment 490, wherein the    visible range is from 400 nm to 700 nm.    Embodiment 492 is the optical system of any of embodiments 466 to    491, wherein the desired plurality of wavelengths comprises an    infrared range of wavelengths.    Embodiment 493 is the optical system of any of embodiments 466 to    492, wherein the desired plurality of wavelengths comprises one or    more of infrared, visible and ultraviolet wavelengths.    Embodiment 494 is the optical system of any of embodiments 466 to    493, wherein the partial reflector is a notch reflector.    Embodiment 495 is the optical system of embodiment 494, wherein the    desired plurality of wavelengths comprises one or more continuous    wavelength ranges, and wherein at least one of the continuous    wavelength ranges has a full width at half maximum of no more than    100 nm.    Embodiment 496 is the optical system of embodiment 495, wherein the    full width at half maximum is no more than 50 nm.    Embodiment 497 is the optical system of any of embodiments 466 to    496, wherein s1/r1 is at least 0.2.    Embodiment 498 is the optical system of any of embodiments 466 to    497, wherein s1/r1 is in a range of 0.2 to 0.8.    Embodiment 499 is the optical system any of embodiments 466 to 498,    wherein s1/r1 is in a range of 0.3 to 0.6.    Embodiment 500 is the optical system of any of embodiments 466 to    499, wherein the reflective polarizer has a second location having a    radial distance, r2, from the optical axis and a displacement, s2,    from the plane, s2/r2 being at least 0.3.    Embodiment 501 is the optical system of any of embodiments 466 to    500, wherein for an area of the reflective polarizer defined by s1    and r1, a maximum variation of a transmission axis of the reflective    polarizer is less than about 2 degrees.    Embodiment 502 is the optical system of any of embodiments 466 to    501 being a beam expander.    Embodiment 503 is a beam expander comprising the optical system of    any of embodiments 466 to 501.    Embodiment 504 is a projection system comprising the beam expander    of embodiment 503 and an image forming device adapted to emit a    patterned light, the projection system configured to direct the    patterned light toward the beam expander.    Embodiment 505 is the projection system of embodiment 504, wherein    the optical system of the beam expander is oriented with the partial    reflector facing the image forming device.    Embodiment 506 is the projection system of embodiment 504 or 505,    further comprising a polarizing beam splitter disposed between the    image forming device and the beam expander.    Embodiment 507 is the projection system of embodiment 506, further    comprising a second reflective polarizer disposed between the beam    expander and the polarizing beam splitter.    Embodiment 508 is the projection system of embodiment 506 or 507,    wherein the polarizing beam splitter comprises first and second    prisms and a flat reflective polarizer disposed between the first    and second prisms along diagonal faces of the first and second    prisms.    Embodiment 509 is the projection system of embodiment 508, wherein    the first prism is disposed between the second prism and the image    forming device.    Embodiment 510 is the projection system of embodiment 508 or 509,    wherein the first prism has a first volume, the second prism has a    second volume, and the first volume is no greater than about half    the second volume.    Embodiment 511 is a projection system comprising the beam expander    of embodiment 503 and an illuminator, the projection system    configured to direct a light output from the illuminator toward the    beam expander.    Embodiment 512 is the projection system of embodiment 511, where the    illuminator comprises:-   a polarizing beam splitter comprising:    -   a first prism having an input face, an output face and a first        hypotenuse;    -   a second prism having an imager face and a second hypotenuse,        the second hypotenuse disposed adjacent the first hypotenuse;        and    -   a second reflective polarizer disposed between the first        hypotenuse and the second hypotenuse;-   a light source disposed adjacent the input face and defining an    input active area on the input face; and-   an image forming device disposed adjacent the imager face for    receiving light emitted from the light source and emitting a    patterned light, the image forming device having a largest image    area, the largest image area defining an output active area on the    output face;-   wherein one or both of the input active area and the output active    area are less than about half the largest image area.    Embodiment 513 is the projection system of embodiment 512, wherein    the input active area is less than about half the largest image    area.    Embodiment 514 is the projection system of embodiment 512, wherein    the output active area is less than about half the largest image    area.    Embodiment 515 is the projection system of embodiment 512, wherein    each of the input active area and the output active area is less    than about half the largest image area.    Embodiment 516 is the projection system of embodiment 512, wherein a    largest surface area of input face is less than about half the    largest image area.    Embodiment 517 is the projection system of embodiment 512, wherein a    largest surface area of the output face is less than about half the    largest image area.    Embodiment 518 is the projection system of embodiment 512, a largest    surface area of input face is less than about half the largest image    area, and wherein a largest surface area of the output face is less    than about half the largest image area.    Embodiment 519 is the projection system of embodiment 512, further    comprising a reflective component disposed adjacent the polarizing    beam splitter opposite the light source.    Embodiment 520 is the projection system of embodiment 512, wherein    the second reflective polarizer is a polymeric multilayer reflective    polarizer, a wire grid polarizer, a MacNeille reflective polarizer,    or a cholesteric reflective polarizer.    Embodiment 521 is the projection system of embodiment 512, wherein    the second reflective polarizer is a polymeric multilayer reflective    polarizer.    Embodiment 522 is the optical system of any of embodiments 1 to 333,    or any of embodiments 378 to 381, or any of embodiments 403 to 475,    wherein the optical system is adapted to provide a dioptric    correction.    Embodiment 523 is the optical system of embodiment 522, wherein the    dioptric correction is adjustable.    Embodiment 524 is a device comprising the optical system of any of    embodiments 1 to 333, or any of embodiments 378 to 381, or any of    embodiments 403 to 523.    Embodiment 525 is the device of embodiment 524 being a head-mounted    display.    Embodiment 526 is the device of embodiment 524 being a beam    expander, an illuminator, or a projector.    Embodiment 527 is the device of embodiment 524 being a camera.    Embodiment 528 is the device of embodiment 524 being a telescope, a    microscope or binoculars.    Embodiment 529 is a head-mounted display comprising a first optical    system, the first optical system being the optical system of any of    embodiments 1 to 333, or any of embodiments 378 to 381, or any of    embodiments 403 to 523.    Embodiment 530 is the head-mounted display of any of embodiments    529, further comprising an eye-tracking system.    Embodiment 531 is the head-mounted display of embodiment 530,    wherein the optical system is adapted to adjust a location of the    reflective polarizer or a location of the partial reflector in    response to signals received from the eye-tracking system.    Embodiment 532 is the head-mounted display of embodiment 529,    further comprising a second optical system, the second optical    system the optical system of any of embodiments 1 to 333, or any of    embodiments 378 to 381, or any of embodiments 403 to 523.    Embodiment 533 is the head-mounted display of embodiment 532,    further comprising an eye-tracking system.    Embodiment 534 is the head-mounted display of embodiment 533,    wherein the optical system is adapted to adjust a location of the    reflective polarizer of the first optical system or a location of    the partial reflector of the first optical system in response to    signals received from the eye-tracking system.    Embodiment 535 is the head-mounted display of embodiment 533 or 534,    wherein the optical system is adapted to adjust a location of the    reflective polarizer of the second optical system or a location of    the partial reflector of the second optical system in response to    signals received from the eye-tracking system.    Embodiment 536 is a head-mounted display comprising:-   a first optical system comprising:    -   a first image surface;    -   a first exit pupil;    -   a first reflective polarizer disposed between the first exit        pupil and the first image surface, the first reflective        polarizer convex about two orthogonal axes;    -   a first partial reflector disposed between the first reflective        polarizer and the first image surface, the first partial        reflector having an average optical reflectance of at least 30%        in a pre-determined plurality of wavelengths; and    -   a first quarter wave retarder disposed between the first        reflective polarizer and the first partial reflector; and-   a second optical system disposed proximate the first optical system,    the second optical system comprising:    -   a second image surface;    -   a second exit pupil;    -   a second reflective polarizer disposed between the second exit        pupil and the second image surface, the second reflective        polarizer convex about two orthogonal axes;    -   a second partial reflector disposed between the second        reflective polarizer and the second image surface, the second        partial reflector having an average optical reflectance of at        least 30% in the pre-determined plurality of wavelengths; and    -   a second quarter wave retarder disposed between the second        reflective polarizer and the second partial reflector.        Embodiment 537 is the head-mounted display of embodiment 536,        wherein an image source comprises the first and second image        surfaces.        Embodiment 538 is the head-mounted display of embodiment 537,        wherein the image source comprises a display panel.        Embodiment 539 is the head-mounted display of embodiment 538,        wherein the display panel is transparent or semi-transparent.        Embodiment 540 is the head-mounted display of any of embodiments        537 to 539, wherein the image source comprises a shutter.        Embodiment 541 is the head-mounted display of embodiment 536,        wherein a first image source comprises the first image surface        and a second image source comprises the second image surface.        Embodiment 542 is the head-mounted display of embodiment 536,        wherein the first image source comprises a first display panel.        Embodiment 543 is the head-mounted display of embodiment 542,        wherein the first display panel is transparent or        semi-transparent.        Embodiment 544 is the head-mounted display of any of embodiments        541 to 543, wherein the first image source comprises a first        shutter.        Embodiment 545 is the head-mounted display of any of embodiments        541 to 544, wherein the second image source comprises a second        display panel.        Embodiment 546 is the head-mounted display of embodiment 545,        wherein the second display panel is transparent or        semi-transparent.        Embodiment 547 is the head-mounted display of any of embodiments        541 to 546, wherein the second image source comprises a second        shutter.        Embodiment 548 is the head-mounted display of any of embodiments        536 to 547, wherein the first and second image surfaces are        substantially planar.        Embodiment 549 is the head-mounted display of any of embodiments        536 to 547, wherein one or both of the first and second image        surfaces are curved.        Embodiment 550 is the head-mounted display of any of embodiments        536 to 549, wherein the first optical system comprises a first        optical lens.        Embodiment 551 is the head-mounted display of embodiment 550,        wherein the first reflective polarizer is disposed on a major        surface of the first optical lens.        Embodiment 552 is the head-mounted display of embodiment 550 or        551, wherein the first optical lens has a non-uniform edge        profile.        Embodiment 553 is the head-mounted display of any of embodiments        536 to 552, wherein the second optical system comprises a second        optical lens.        Embodiment 554 is the head-mounted display of embodiment 553,        wherein the second reflective polarizer is disposed on a major        surface of the second optical lens.        Embodiment 555 is the head-mounted display of embodiment 553 or        554, wherein the second optical lens has a non-uniform edge        profile.        Embodiment 556 is the head-mounted display of any of embodiments        536 to 555, wherein the first reflective polarizer is the        thermoformed multilayer reflective polarizer of any of        embodiments 334 to 353.        Embodiment 557 is the head-mounted display of any of embodiments        536 to 556, wherein the second reflective polarizer is the        thermoformed multilayer reflective polarizer of any of        embodiments 334 to 353.        Embodiment 558 is the head-mounted display of any of embodiments        536 to 557, further comprising an eye-tracking system.        Embodiment 559 is the head-mounted display of embodiment 558,        wherein the first optical system is adapted to adjust a distance        between the first reflective polarizer and the first partial        reflector in response to signals received from the eye-tracking        system.        Embodiment 560 is the head-mounted display of embodiment 558 or        embodiment 559, wherein the second optical system is adapted to        adjust a distance between the second reflective polarizer and        the second partial reflector in response to signals received        from the eye-tracking system.        Embodiment 561 is the head-mounted display of any of embodiments        536 to 560, wherein the pre-determined plurality of wavelengths        comprise at least one continuous wavelength range.        Embodiment 562 is the head-mounted display of any of embodiments        536 to 561, wherein the pre-determined plurality of wavelengths        comprises a visible range of wavelengths.        Embodiment 563 is the head-mounted display of embodiment 562,        wherein the visible range is from 400 nm to 700 nm.        Embodiment 564 is the head-mounted display of any of embodiments        536 to 563, wherein the pre-determined plurality of wavelengths        comprises an infrared range of wavelengths.        Embodiment 565 is the head-mounted display of any of embodiments        536 to 564, wherein the pre-determined plurality of wavelengths        comprises one or more of infrared, visible and ultraviolet        wavelengths.        Embodiment 566 is the head-mounted display of any of embodiments        536 to 565, wherein the partial reflector is a notch reflector.        Embodiment 567 is the head-mounted display of embodiment 566,        wherein the pre-determined plurality of wavelengths comprises        one or more continuous wavelength ranges, and wherein at least        one of the continuous wavelength ranges has a full width at half        maximum of no more than 100 nm.        Embodiment 568 is the head-mounted display of embodiment 566,        wherein the pre-determined plurality of wavelengths comprises        one or more continuous wavelength ranges, and wherein at least        one of the continuous wavelength ranges has a full width at half        maximum of no more than 50 nm.        Embodiment 569 is the head-mounted display of any of embodiments        536 to 568, wherein the first optical system is the optical        system of any of embodiments 1 to 333, or any of embodiments 378        to 381, or any of embodiments 403 to 523.        Embodiment 570 is the head-mounted display of any of embodiments        536 to 569, wherein the second optical system is the optical        system of any of embodiments 1 to 333, or any of embodiments 378        to 381, or any of embodiments 403 to 523.        Embodiment 571 is the head-mounted display of any of embodiments        529 to 570 being a virtual reality display.        Embodiment 572 is a camera comprising:-   an aperture;-   an image recording device;-   a reflective polarizer disposed between the aperture and the image    recording device, the reflective polarizer curved about two    orthogonal axes;-   a partial reflector disposed between the reflective polarizer and    the image recording device, the partial reflector having a having an    average optical reflectance of at least 30% in a pre-determined    plurality of wavelengths; and-   a quarter wave retarder disposed between the reflective polarizer    and the partial reflector.    Embodiment 573 is the camera of embodiment 572 further comprising a    first optical stack, the first optical stack including a first lens    and the partial reflector.    Embodiment 574 is the camera of embodiment 572 or 573 further    comprising a second optical stack, the second optical stack    including a second lens and the reflective polarizer.    Embodiment 575 is the camera of embodiment 572 further comprising an    integral optical stack, the integral optical stack comprising a    first optical lens, the reflective polarizer, the partial reflector    and the quarter wave retarder.    Embodiment 576 is the camera of embodiment 575, wherein the integral    optical stack further comprises a second optical lens adjacent the    first optical lens, the quarter wave retarder disposed between the    first and second optical lenses, the partial reflector disposed on a    major surface of the first optical lens opposite the second optical    lens, and the reflective polarizer disposed on a major surface of    the second optical lens opposite the first optical lens.    Embodiment 577 is the camera of any of embodiments 572 to 576,    wherein at least one first location on the reflective polarizer has    a radial distance r1 from an optical axis of the reflective    polarizer and a displacement s1 from a plane perpendicular to the    optical axis at an apex of the reflective polarizer, s1/r1 being at    least 0.1.    Embodiment 578 is the camera of embodiment 577, wherein s1/r1 is at    least 0.2.    Embodiment 579 is the camera of any of embodiments 577 to 578,    wherein the reflective polarizer comprises at least one layer    substantially optically biaxial at at least one first location on    the at least one layer away from the optical axis and substantially    optically uniaxial at at least one second location away from the    optical axis.    Embodiment 580 is the camera of any of embodiments 572 to 579,    wherein the reflective polarizer is thermoformed APF.    Embodiment 581 is the camera of any of embodiments 572 to 578,    wherein the reflective polarizer is a wire grid polarizer.    Embodiment 582 is the camera of any of embodiments 572 to 581,    wherein the reflective polarizer is convex towards the image    recording device.    Embodiment 583 is the camera of embodiment 572, wherein the camera    comprises an optical system, the optical system including the    reflective polarizer, the quarter wave retarder and the partial    reflector, an image surface and a stop surface, the image surface    being a surface of the image recording device and the stop surface    being a surface defined by the aperture.    Embodiment 584 is the camera of embodiment 583 wherein the optical    system is further characterized by any of embodiments 1 to 333, or    any of embodiments 378 to 381, or any of embodiments 403 to 523.    Embodiment 585 is a beam expander comprising:-   a partial reflector having a having an average optical reflectance    of at least 30% in a pre-determined plurality of wavelengths;-   a reflective polarizer disposed adjacent to and spaced apart from    the partial reflector, the reflective polarizer curved about two    orthogonal axes; and-   a quarter wave retarder disposed between the reflective polarizer    and the partial reflector.    Embodiment 586 is the beam expander of embodiment 585, wherein the    beam expander is adapted to receive converging light incident on the    partial reflector and transmit diverging light through the    reflective polarizer.    Embodiment 587 is the beam expander of embodiment 585 or 586 further    comprising a first optical stack, the first optical stack including    a first lens and the partial reflector.    Embodiment 588 is the beam expander of any of embodiments 585 to    587, further comprising a second optical stack, the second optical    stack including a second lens and the reflective polarizer.    Embodiment 589 is the beam expander of embodiment 585 or 586 further    comprising an integral optical stack, the integral optical stack    comprising a first optical lens, the reflective polarizer, the    partial reflector and the quarter wave retarder.    Embodiment 590 is the beam expander of embodiment 589, wherein the    integral optical stack further comprises a second optical lens    adjacent the first optical lens, the quarter wave retarder disposed    between the first and second optical lenses, the partial reflector    disposed on a major surface of the first optical lens opposite the    second optical lens, and the reflective polarizer disposed on a    major surface of the second optical lens opposite the first optical    lens.    Embodiment 591 is the beam expander of any of embodiments 585 to    590, wherein at least one first location on the reflective polarizer    has a radial distance r1 from an optical axis of the reflective    polarizer and a displacement s1 from a plane perpendicular to the    optical axis at an apex of the reflective polarizer, s1/r1 being at    least 0.1.    Embodiment 592 is the beam expander of embodiment 591, wherein s1/r1    is at least 0.2.    Embodiment 593 is the beam expander of any of embodiments 585 to    592, wherein the reflective polarizer comprises at least one layer    substantially optically biaxial at at least one first location on    the at least one layer away from the optical axis and substantially    optically uniaxial at at least one second location away from the    optical axis.    Embodiment 594 is the beam expander of any of embodiments 585 to    593, wherein the reflective polarizer is thermoformed APF.    Embodiment 595 is the beam expander of any of embodiments 585 to    592, wherein the reflective polarizer is a wire grid polarizer.    Embodiment 596 is a projection system comprising a light source, an    image forming device disposed to receive light from the light source    and emit a patterned light, and the beam expander of any of    embodiments 585 to 595 disposed such that the patterned light from    the image forming device is incident on the partial reflector.    Embodiment 597 is the projection system of embodiment 596, further    comprising a polarizing beam splitter disposed between the image    forming device and the beam expander.    Embodiment 598 is a projection system comprising a light source, an    image forming device disposed to receive light from the light source    and emit a converging patterned light, and a beam expander, the beam    expander comprising:-   a partial reflector having a having an average optical reflectance    of at least 30% in a pre-determined plurality of wavelengths;-   a reflective polarizer disposed adjacent to and spaced apart from    the partial reflector, the reflective polarizer curved about two    orthogonal axes; and-   a quarter wave retarder disposed between the reflective polarizer    and the partial reflector,-   wherein the beam expander is disposed such that the converging    patterned light from the image forming device is incident on the    partial reflector, the beam expander transmitting a diverging    patterned light.    Embodiment 599 is the projections system of embodiment 598, wherein    the beam expander is further characterized by any of embodiments 586    to 595.    Embodiment 600 is the projections system of embodiment 598 or 599    further comprising a polarizing beam splitter disposed between the    image forming device and the beam expander.    Embodiment 601 is an illuminator comprising:-   a beam expander comprising a reflective polarizer curved about two    orthogonal directions;-   a polarizing beam splitter comprising:    -   a first prism having an input face, an output face and a first        hypotenuse;    -   a second prism having a first face and a second hypotenuse, the        second hypotenuse disposed adjacent the first hypotenuse; and    -   a second reflective polarizer disposed between the first        hypotenuse and the second hypotenuse;-   a light source disposed adjacent the input face and defining an    input active area on the input face; and-   a reflective component disposed adjacent the first face for    receiving light emitted from the light source and emitting a    converging light, the reflective component having a largest active    area, the largest active area defining an output active area on the    output face;-   wherein the beam expander disposed to receive the converging light    and transmit a diverging light, and one or both of the input active    area and the output active area are less than about half the largest    active area of the reflective component.    Embodiment 602 is the illuminator of embodiment 601, wherein the    beam expander further comprises a partial reflector adjacent to and    spaced apart from the reflective polarizer, the partial reflector    having an average optical reflectance of at least 30% in a    pre-determined plurality of wavelengths, the partial reflector    disposed between the polarizing beam splitter and the reflective    polarizer.    Embodiment 603 is the illuminator of embodiment 602 further    comprising a quarter wave retarder disposed between the reflective    polarizer and the partial reflector.    Embodiment 604 is the illuminator of any of embodiments 601 to 603,    wherein the beam expander is further characterized by any of    embodiments 585 to 595.    Embodiment 605 is the illuminator of any of embodiments 601 to 604,    wherein the reflective component is an image forming device.    Embodiment 606 is the illuminator of any of embodiments 601 to 605    being an image projector.    Embodiment 607 is a magnifying device comprising an optical system,    the optical system comprising:-   an exit pupil;-   a reflective polarizer proximate the exit pupil, the reflective    polarizer curved about two orthogonal axes;-   a partial reflector disposed adjacent the reflective polarizer    opposite the exit pupil, the partial reflector spaced apart from the    reflective polarizer; the partial reflector having a having an    average optical reflectance of at least 30% in a pre-determined    plurality of wavelengths; and-   a quarter wave retarder disposed between the reflective polarizer    and the partial reflector.    Embodiment 608 is the magnifying device of embodiment 607, wherein    the optical system is further characterized by any of embodiments 1    to 333, or any of embodiments 378 to 381, or any of embodiments 403    to 523.    Embodiment 609 is the magnifying device of embodiment 607 or 608    further comprising an objective portion and an eyepiece portion.    Embodiment 610 is the magnifying device of embodiment 609, wherein    the objective portion comprises the reflective polarizer, the    partial reflector and the quarter wave retarder.    Embodiment 611 is the magnifying device of embodiment 609, wherein    the eyepiece portion comprises the optical system.    Embodiment 612 is the magnifying device of any of embodiments 607 to    611, wherein the optical system further comprises a first optical    stack, the first optical stack including a first lens and the    partial reflector.    Embodiment 613 is the magnifying device of any of embodiments 607 to    612, wherein the optical system further comprises a second optical    stack, the second optical stack including a second lens and the    reflective polarizer.    Embodiment 614 is the magnifying device of any of embodiments 607 to    611, wherein the optical system further comprises an integral    optical stack, the integral optical stack comprising a first optical    lens, the reflective polarizer, the partial reflector and the    quarter wave retarder.    Embodiment 615 is the magnifying device of embodiment 614, wherein    the integral optical stack further comprises a second optical lens    adjacent the first optical lens, the quarter wave retarder disposed    between the first and second optical lenses, the partial reflector    disposed on a major surface of the first optical lens opposite the    second optical lens, and the reflective polarizer disposed on a    major surface of the second optical lens opposite the first optical    lens.    Embodiment 616 is the magnifying device of any of embodiments 607 to    615, being binoculars, a telescope or a microscope.    Embodiment 617 is the magnifying device of any of embodiments 607 to    616, wherein at least one first location on the reflective polarizer    has a radial distance r1 from an optical axis of the reflective    polarizer and a displacement s1 from a plane perpendicular to the    optical axis at an apex of the reflective polarizer, s1/r1 being at    least 0.1.    Embodiment 618 is the magnifying device of embodiment 617, wherein    s1/r1 is at least 0.2.    Embodiment 619 is the magnifying device of any of embodiments 607 to    618, wherein the reflective polarizer comprises at least one layer    substantially optically biaxial at at least one first location on    the at least one layer away from the optical axis and substantially    optically uniaxial at at least one second location away from the    optical axis.    Embodiment 620 is the magnifying device of any of embodiments 607 to    619, wherein the reflective polarizer is thermoformed APF.    Embodiment 621 is the magnifying device of any of embodiments 607 to    618, wherein the reflective polarizer is a wire grid polarizer.

Unless otherwise indicated, all numbers expressing quantities,measurement of properties, and so forth used in the specification andclaims are to be understood as being modified by the term “about”.Accordingly, unless indicated to the contrary, the numerical parametersset forth in the specification and claims are approximations that canvary depending on the desired properties sought to be obtained by thoseskilled in the art utilizing the teachings of the present application.Not as an attempt to limit the application of the doctrine ofequivalents to the scope of the claims, each numerical parameter shouldat least be construed in light of the number of reported significantdigits and by applying ordinary rounding techniques. Notwithstandingthat the numerical ranges and parameters setting forth the broad scopeof the invention are approximations, to the extent any numerical valuesare set forth in specific examples described herein, they are reportedas precisely as reasonably possible. Any numerical value, however, maywell contain errors associated with testing or measurement limitations.

Descriptions for elements in figures should be understood to applyequally to corresponding elements in other figures, unless indicatedotherwise or unless the context clearly indicates otherwise. Althoughspecific embodiments have been illustrated and described herein, it willbe appreciated by those of ordinary skill in the art that a variety ofalternate and/or equivalent implementations can be substituted for thespecific embodiments shown and described without departing from thescope of the present disclosure. This application is intended to coverany adaptations or variations of the specific embodiments discussedherein. Therefore, it is intended that this disclosure be limited onlyby the claims and the equivalents thereof.

What is claimed is:
 1. An optical system, comprising: a partialreflector having an average optical reflectance of at least 30% in adesired plurality of wavelengths; a reflective polarizer curved abouttwo orthogonal axes and substantially transmitting light having a firstpolarization state and substantially reflecting light having anorthogonal second polarization state, at least one location on thereflective polarizer having a radial distance r1 from an optical axispassing through an apex of the reflective polarizer and a displacements1 from a plane perpendicular to the optical axis at the apex of thereflective polarizer, s1/r1 being at least 0.1; and a first quarter waveretarder disposed between the partial reflector and the reflectivepolarizer, wherein the optical system is adapted to provide anadjustable shape of at least one surface of the optical system.
 2. Theoptical system of claim 1, wherein the at least one surface comprises asurface of the partial reflector.
 3. The optical system of claim 2,wherein a first optical stack comprises the partial reflector and theadjustable shape of the at least one surface is provided, at least inpart, by an adjustable shape of the first optical stack.
 4. The opticalsystem of claim 1, wherein the at least one surface comprises a surfaceof the reflective polarizer.
 5. The optical system of claim 4, wherein asecond optical stack comprises the reflective polarizer and theadjustable shape of the at least one surface is provided, at least inpart, by an adjustable shape of the second optical stack.
 6. The opticalsystem of claim 1, wherein the reflective polarizer comprises at leastone layer substantially optically biaxial at at least one first locationon the at least one layer away from the optical axis and substantiallyoptically uniaxial at at least one second location away from the opticalaxis.
 7. The optical system of claim 1, wherein s1/r1 is in a range of0.2 to 0.8.
 8. An optical system, comprising: a partial reflector havingan average optical reflectance of at least 30% in a desired plurality ofwavelengths; a reflective polarizer curved about two orthogonal axes andsubstantially transmitting light having a first polarization state andsubstantially reflecting light having an orthogonal second polarizationstate, at least one location on the reflective polarizer having a radialdistance r1 from an optical axis passing through an apex of thereflective polarizer and a displacement s1 from a plane perpendicular tothe optical axis at the apex of the reflective polarizer, s1/r1 being atleast 0.1; and a first quarter wave retarder disposed between thepartial reflector and the reflective polarizer, wherein the opticalsystem is adapted to provide an adjustable focus.
 9. The optical systemof claim 8, wherein the adjustable focus is provided, at least in part,by an adjustable distance between two surfaces in the optical system.10. The optical system of claim 9, wherein the two surfaces comprise asurface of the reflective polarizer and a surface of the partialreflector.
 12. The optical system of claim 8, wherein a first opticalstack comprises the partial reflector, and the adjustable focus isprovided, at least in part, by an adjustable shape of the first opticalstack.
 12. The optical system of claim 8, wherein a second optical stackcomprises the reflective polarizer, and the adjustable focus isprovided, at least in part, by an adjustable shape of the second opticalstack.
 13. The optical system of claim 8, wherein the reflectivepolarizer comprises at least one layer substantially optically biaxialat at least one first location on the at least one layer away from theoptical axis and substantially optically uniaxial at at least one secondlocation away from the optical axis.
 14. The optical system of claim 8,wherein s1/r1 is in a range of 0.2 to 0.8.
 15. An optical system,comprising: a partial reflector having an average optical reflectance ofat least 30% in a desired plurality of wavelengths; a reflectivepolarizer curved about two orthogonal axes and substantiallytransmitting light having a first polarization state and substantiallyreflecting light having an orthogonal second polarization state, atleast one location on the reflective polarizer having a radial distancer1 from an optical axis passing through an apex of the reflectivepolarizer and a displacement s1 from a plane perpendicular to theoptical axis at the apex of the reflective polarizer, s1/r1 being atleast 0.1; and a first quarter wave retarder disposed between thepartial reflector and the reflective polarizer, wherein the opticalsystem is adapted to provide an adjustable distance between two surfacesof the optical system.
 16. The optical system of claim 15, wherein thetwo surfaces comprise a surface of the reflective polarizer and asurface of the partial reflector.
 17. The optical system of claim 15,wherein a first optical stack comprises the partial reflector and asecond optical stack comprises the reflective polarizer.
 18. The opticalsystem of claim 17, wherein the two surfaces comprise a surface of thefirst optical stack and a surface of the second optical stack.
 19. Theoptical system of claim 15, wherein the reflective polarizer comprisesat least one layer substantially optically biaxial at at least one firstlocation on the at least one layer away from the optical axis andsubstantially optically uniaxial at at least one second location awayfrom the optical axis.
 20. The optical system of claim 15, wherein s1/r1is in a range of 0.2 to 0.8.
 21. A head-mounted display comprising afirst optical system according to claim 15, a second optical systemaccording to claim 15, and an eye-tracking system, the head-mounteddisplay being adapted to stereoscopically present first and secondvirtual images of an object to a viewer through the respective first andsecond optical systems, the eye-tracking system being configured todetect a viewing direction, wherein the head-mounted display is adaptedto adjust first and second virtual image distances of the respectivefirst and second virtual images to match a depth of the object aspresented stereoscopically in the viewing direction by adjusting theadjustable distance between the two surfaces of at least one of thefirst and second optical systems.